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2020-10-15T20:17:57Z

BertJonson64: Created page with "{{High School |name= |type= |city= |students= |sports= |colors= |mascot= }}"

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Pi

2020-10-15T19:51:13Z

BertJonson64: new mathematical applications

'''Pi''', or '''[[Archimedes]]' constant''', is perhaps the most important [[mathematics|mathematical]] constant in all of [[mathematics]] and engineering. It is defined as the [[ratio]] of the [[circumference]] of a [[circle]] to its [[diameter]], and represented by the 16th letter of the Greek alphabet, '''<big><math>\pi</math></big>'''. It was first used with its current meaning in 1706 by a Welsh mathematician William Jones,<ref name="hist">{{cite web
| url = http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Pi_through_the_ages.html
| title = A history or Pi
| accessdate = 2012-02-11}}</ref> who selected '''<big><math>\pi</math></big>''' because it is the first letter of the Greek word for [[perimeter]] (''περίμετρος''), i.e. the circumference of a circle is its perimeter. A Swiss mathematician, [[Leonhard Euler]], brought the concept into general use in 1737.

<big><math>\pi</math></big> is referenced in the [[Bible]], literature, and even as the title of a movie. It is central to the most famous identity in all of mathematics: [[Euler's Formula|Euler's Identity]].

The value of '''<big><math>\pi</math></big>''' is approximately 3.1416, or 22/7. The exact value cannot be expressed as a [[fraction]] or as a [[decimal]] number, regardless of how many [[digit]]s are used. Johann Heinrich Lambert proved this in 1761 by showing that '''<big><math>\pi</math></big>''' is an [[irrational number]], which means that it can't be expressed as a fraction.<ref>{{cite web
| url = http://turnbull.mcs.st-and.ac.uk/~history/Biographies/Lambert.html
| title = Biography of Johann Heinrich Lambert
| accessdate = 2012-02-12}}</ref> In 1882, Carl Louis Ferdinand von Lindeman proved that '''<big><math>\pi</math></big>''' is also a [[transcendental number]], which means that it can't be expressed as the solution to any simple [[equation]].<ref>{{cite web
| url = http://turnbull.mcs.st-and.ac.uk/~history/Biographies/Lindemann.html
| title = Biography of Carl Louis Ferdinand von Lindemann
| accessdate = 2012-02-12}}</ref>

==History==
Mathematicians have worked for centuries to calculate '''<big><math>\pi</math></big>''' to more and more decimal places. To some extent, the progress of mathematics, or at least of computation, can be gauged by the progress in the number of digits to which '''<big><math>\pi</math></big>''' has been calculated.

Some ancients expressed '''<big><math>\pi</math></big>''' by using fractional approximations. The Rhind, or Ahmes Papyrus (''c.'' 1650 B.C.)<ref>http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html</ref><ref>https://www.math.tamu.edu/~don.allen/history/egypt/node3.html</ref> has shown that the [[ancient Egypt]]ians had determined the value for '''<big><math>\pi</math></big>''' to be 3.1605. The [[Babylonia]]n value from the same era was 3 1/8 = 3.125.<ref>Boyer, ''A History of Mathematics'', 2nd edition</ref>, coming to within 1 percent accuracy for both<ref>https://www.maa.org/press/periodicals/convergence/mathematical-treasure-old-babylonian-area-calculation</ref>.

[[Archimedes]] of Syracuse (287-212 BC) carried out "the first theoretical calculation" of '''<big><math>\pi</math></big>'''.<ref>[http://veling.nl/anne/templars/Pi_through_the_ages.html Pi through the ages]</ref>, using regular polygons with a total of 96 sides, within and circumscribing a circle, and in about 225 B.C. he came up with a formula between the folowing numbers:
<center><math>3 \dfrac {1} {7} < \pi < 3 \dfrac {10} {71}</math></center>

This is ten times better than the Egyptian and Babylonian values, and it is within 0.04 percent of the correct value. The German-Dutch mathematician Ludolph Van Ceulen used Archimedes's formula to calculate '''<big><math>\pi</math></big>''' to 32 digits in 1615. He was so proud of his achievement that he had the digits engraved on his tombstone<ref>https://www.ams.org/publicoutreach/math-history/hap-6-pi.pdf</ref>.

Towards the end of the 17th century mathematical analysis had new methods of making calculations, and '''<big><math>\pi</math></big>''' was no exception. Brilliant mathematicians had made individual calculations for '''<big><math>\pi</math></big>''' in a variety of ways. In 1593 [[François Viète]] (1540-1603) wrote the expression:

<center><math>\pi = 2 \times \dfrac 2 {\sqrt 2} \times \dfrac 2 {\sqrt {2 + \sqrt 2} } \times \dfrac 2 {\sqrt {2 + \sqrt {2 + \sqrt 2} } } \times \dfrac 2 {\sqrt {2 + \sqrt {2 + \sqrt {2 + \sqrt 2 } } } } \times \cdots</math></center>

[[John Wallis]] (1616-1703) made his expression 1655, proving that:
<center><math>\frac{\pi}{2} = \frac21\cdot\frac23\cdot\frac43\cdot\frac45\cdot\frac65\cdot\frac67\cdots</math></center>

[[William Brouncker]] (1620-1684) discovered the continued fraction in 1658:
<center><math>
\frac \pi 4 = \cfrac{1}{1+\cfrac{1^2}{2+\cfrac{3^2}{2+\cfrac{5^2}{2+\cfrac{7^2}{2+\cfrac{9^2}{2+\ddots}}}}}}
</math></center>

During the plague of 1665-1666, [[Isaac Newton]] was confined to the English village of Woolsthorpe. There he calculated '''<big><math>\pi</math></big>''' to 16 digits.

<center><math>\pi = \dfrac {3 \sqrt 3} 4 + 24 \left({\dfrac 1 {12} - \dfrac 1 {5 \times 2^5} - \dfrac 1 {28 \times 2^7} - \dfrac 1 {72 \times 2^9} - \cdots}\right)</math></center>

Unlike Van Ceulen, Newton did not consider his calculations to be an achievement. "I am ashamed to tell you to how many figures I carried these computations, having no other business at the time," he wrote.<ref>Beckmann, Petr (2015-01-06). ''A History of Pi'' (Kindle Locations 2249-2250). St. Martin's Press. Kindle Edition.</ref>

[[Gottfried Leibniz|Gottfried Wilhelm von Leibniz]] (1646-1716) published a series for '''<big><math>\pi</math></big>''' in 1673, coming up with the formulas:
<center><math>\dfrac \pi 4 = 1 - \dfrac 1 3 + \dfrac 1 5 - \dfrac 1 7 + \dfrac 1 9 - \cdots \approx 0.78539 \, 81633 \, 9744 \ldots</math><ref>https://oeis.org/A003881</ref></center>

<center><math>\displaystyle \pi = 4 \sum_{k \mathop \ge 0} \left({-1}\right)^k \frac 1 {2 k + 1}</math></center>

Brouncker's convergents are related to the [[Leibniz formula for pi]]: for instance
<center><math>
\frac{1}{1+\frac{1^2}{2}} = \frac{2}{3} = 1 - \frac{1}{3}
</math>
and
:<math>
\frac{1}{1+\frac{1^2}{2+\frac{3^2}{2}}} = \frac{13}{15} = 1 - \frac{1}{3} + \frac{1}{5}.
</math></center>

In 1706, John Machin, secretary of [[England]]'s Royal Society, developed a quickly converging formula for '''<big><math>\pi</math></big>''' and used it to calculated the first 100 digits. In 1844, the idiot savant Johann Dase of [[Hamburg]] used Machin's formula to calculate 200 digits in less than two months.<ref>Beckmann</ref> In contrast, William Shanks spent twenty years calculating '''<big><math>\pi</math></big>''' to 707 places, a task he completed in 1873. In 1945, it was discovered that only the first 527 of Shanks's digits were correct.

ENIAC, the first electronic [[computer]], took seventy hours to calculate 2,037 digits in 1949. In 2008, the first million digits of '''<big><math>\pi</math></big>''' were published on [[Project Gutenberg]].<ref>Hemphill, Scott, ''[https://www.gutenberg.org/ebooks/50 Pi to 1,000,000 places]''.</ref> In 2014, the anonymous programmer Houkouonchi calculated the first 13.3 trillion digits of '''<big><math>\pi</math></big>''' in 208 days.<ref>Yee, Alexander, "[http://www.numberworld.org/y-cruncher/ y-cruncher - A Multi-Threaded Pi-Program]"</ref> This result has not been published.

=='''<big><math>\pi</math></big>''' in mathematics==
It's impossible to overestimate the importance of '''<big><math>\pi</math></big>''' (and ''[[e]]'') for mathematics. These values are tied by [[Euler's Formula|Euler's identity]]:

:<math>e^{\pi \imath} +1 = 0</math>.

'''<big><math>\pi</math></big>''' may be used to determine the area of a circle:<ref>{{cite web
| url = http://www.worsleyschool.net/science/files/circle/area.html
| title = The Circle Area Formula
| accessdate = 2012-02-13}}</ref>

:<big><math>Area= \pi r^{2}</math></big>

Another interesting aspect of '''<big><math>\pi</math></big>''' is that any given number multiplied by it will be infinitely large because '''<big><math>\pi</math></big>''' is infinitely long.

==Recreation==
Memorizing '''<big><math>\pi</math></big>''' is a challenge that appeals to some people. Mnemonics have been devised. Counting the letters in each word of the phrase "Now I want a drink—alcoholic, of course" gives '''<big><math>\pi</math></big>''' to seven places (which is more than enough for all ordinary purposes). Numerous other mnemonics of this kind have been devised; in 1995, Michael Keith wrote one entitled [http://users.aol.com/s6sj7gt/mikerav.htm Near a Raven] which simultaneously parodies [[Edgar Allen Poe]]'s poem ''The Raven,'' while encoding '''<big><math>\pi</math></big>''' to 740 places.

March 14 marks [[Pi Day]], a holiday on which the mathematical constant is celebrated. The date, 3/14, comes from the first three digits of '''<big><math>\pi</math></big>'''. Some people begin their celebration at 1:59 pm, derived from the following three digits.

Pi Approximation Day is a similar holiday, celebrated on 22 July (from the approximation 22/7).<ref>[https://www.usatoday.com/tech/science/mathscience/2007-03-14-pi-day_N.htm USA Today (3/14/2007) - Pi-day]</ref>

The value of pi is approximately:

{{quotebox|
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692...}}

Many Christians are sceptical to use '''<big><math>\pi</math></big>''' due to it often being symbolised by an ancient Greek symbol. The ancient Greeks were of course occult and their belives challenge American Christian belevives. American conservatives are therefore advised to write you pi instead of '''<big><math>\pi</math></big>'''.

==Does the Bible attempt to define pi?==
Virtually all serious students of the [[Bible]] say no. Still, critics frequently claim that the Bible contains an incorrect value for '''<big><math>\pi</math></big>''', and the question is raised frequently enough to earn mention in the [[Skeptics Annotated Bible]].

The claim is based on a verse in the [[I Kings|first book of Kings]]:
{{bible quote|He made the Sea of cast metal, circular in shape, measuring ten [[cubit]]s from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.|book=1_Kings|chap=7|verses=23|version=NIV}} Thus, critics say, the Bible claims that the value of '''<big><math>\pi</math></big>''' is three, and is therefore in error. However, there are a number of assumptions in this claim, any of which might invalidate the argument if wrong:

* That the tools and system of measurement available to the builders were sufficiently accurate to distinguish between three and '''<big><math>\pi</math></big>'''.
* That the phrase translated as "circular in shape" means perfectly circular, not simply "round" as an ellipse is round.
* That the Bible is trying to provide a value for '''<big><math>\pi</math></big>''', and not merely describing the historical event of building this object.<ref name="math">{{cite web
| url = http://mathforum.org/library/drmath/view/52573.html
| title = Discussion re rounding Pi
| accessdate = 2012-02-10}}</ref>
* That a value is ''wrong'' simply because it depends on imprecisely expressed divisors. The ratio that is '''<big><math>\pi</math></big>''' can be derived completely accurately for a whole range of values<ref name="math" /> even if the Sea is taken as a perfect circle, namely when, before rounding to the nearest [[whole number]], the diameter is known to be greater than 9.5 and less than about 9.708, and the circumference greater than about 29.845 and less than 30.5, it being quite common at the time to round to whole numbers.<ref name="jph">{{cite web
| url = http://www.tektonics.org/lp/piwrong.html
| title = Is the Bible wrong about pi?
| accessdate = 2012-02-10}}</ref>
* That both the [[diameter]] and the [[circumference]] are measuring the same edges. Since the sides of any practical vessel have thickness, it is possible that the diameter is an outside measurement and the circumference is an inside measurement.<ref name="jph" />
* That both the diameter and the circumference are measuring the same part of the object. The object is also described as having an outward-turned rim. The easiest places to measure the diameter would be across the wider rim, and the easiest place to measure the circumference would be around the body below the rim.<ref>{{cite web
| url = http://creationontheweb.com/content/view/1731/
| title = Does the Bible say Pi equals 3.0?
| accessdate = 2012-02-10}}</ref>

Common sense and a rudimentary knowledge of the Bible should cause one to question whether it sets out to define mathematical concepts. The creation of a "sea of cast metal" by human beings in ancient times, without modern construction tools and measuring equipment, does not require nor could it utilize a precise value for '''<big><math>\pi</math></big>'''. An even more fundamental objection is that '''<big><math>\pi</math></big>''' is an [[irrational number]], and therefore has an infinite number of digits. (A "closed form" of '''<big><math>\pi</math></big>''' does exist, but requires mathematical notation that was invented many centuries later.) A decimal expression of '''<big><math>\pi</math></big>''' could not "fit" in the Bible, or in any other finite text.<ref name="math" />

==References==
<small><references/></small>

==See also==
*[[Pi Day]]
*[http://yacas.sourceforge.net/Algochapter5.html#c5s5 Calculation of pi with computers]

[[Category:Mathematics]]

Integral

2020-10-15T19:34:58Z

BertJonson64: additional perspectives

{{Math-h}}

An '''integral''' is a mathematical construction used in [[calculus]] to represent the area of a region in a plane bounded by the graph of a [[function]] in one [[real]] variable. [[Definite integral]]s use the following notation:

:<math>\int_a^b f(x)dx</math>

where ''a'' and ''b'' represent the lower and upper bounds of the [[interval]] being integrated over, ''f(x)'' represents the function being integrated (the '''integrand'''), and ''dx'' represents a dummy variable given various definitions, depending on the context of the integral.

[[Image:Definiteintegralnv7.gif|thumb|A definite integral.]]

[[Indefinite integral]]s use the notation
:<math>\int f(x) dx </math>

==Integration==
===Definition===
If <math> f</math> is a function of bounded variation, then the [[Riemann integral]] of <math> f</math> is defined as the limit of a [[Riemann sum]]:
:<math>\int\limits_{x_1}^{x_N} f(x) dx = \lim_{dx\to 0} \sum_{i=1}^N f(x_i)*dx</math>.

The fact that <math> f </math> is of bounded variation implies that the Riemann sum above converges and is independent of the choices of <math>x_1,\dots,x_N</math>. For integration of measurable functions which may not have bounded variation, the [[Lebesgue integral]] must be used. It is easy to see that <math>\int\limits_a^b f(x) dx</math> is the area under the curve f(x) between the vertical line x=a and the vertical line x=b. <tt>a</tt> and <tt>b</tt> are called the ''limits'' of the integral, and <tt>f(x)</tt> is called the ''integrand''. This type of integral is referred to as a ''definite integral'', or an integral between definite limits.

Indefinite integrals are related to definite integrals by the second part of the [[Fundamental Theorem of Calculus]].

===Applications===
The first part of the [[Fundamental Theorem of Calculus]] states that integration is the reverse function of [[Derivative (calculus)|differentiation]]. Thus, if <math>\int f(x) dx = g(x)</math>, then <math>\frac{d}{dx}g(x) = f(x)</math>.

Note that, because the derivative of any constant function is 0, <math>\frac{d}{dx}x^2+2 = \frac{d}{dx}x^2+3 = \frac{d}{dx}x^2 = 2x</math>. Therefore, <math>\int 2x dx</math> does not simply equal x<sup>2</sup>, but rather x<sup>2</sup> + C for any constant real number C. The above-mentioned functions are the ''family of antiderivatives'' for 2x.

The concept of integration can be extended to functions in more than one real variable, as well as functions defined over the [[complex numbers]].

Integration has many physical applications. The indefinite integral of an [[acceleration]] function with respect to time gives the [[velocity]] function defined to within a constant, while the definite integral of an acceleration function with respect to time gives the change in velocity between the upper and lower limits of integration. Likewise, the indefinite integral of a time function of velocity with respect to time gives the position function defined to within a constant, and the definite integral of this velocity function will give the change in position between the two limits of integration.

=== Methods of Integration ===
{{main|Methods of integration}}
There are many different ways to integrate functions. Sometimes, when it is impossible to directly integrate a function, an approximation is used, such as the Riemann integral. Or, there may be a process to integrate the function using a rule, such as with [[Integration by parts]].

==Types of Integrals==

There are several types of integrals. [[Definite integral]]s are integrals that are evaluated over limits of integration. [[Indefinite integral]]s are not evaluated over limits of integration. Evaluating an indefinite integral yields the antiderivative of the integrand plus a constant of integration.

A third type - an improper integral - is an integral in which one of the limits of integration is infinity. Evaluating an improper integral requires taking the limit of the definite integral as the appropriate limit of integration approaches infinity.

A fourth type of integral is known as the Lebesgue integral. The Lebesgue integral is a generalization of the Riemann integral that allows traditionally and non-integrable functions such as the indicator function on the rational numbers to be integrated.
==Properties of integrals==

Integration has the following properties<ref>[http://www.sosmath.com/calculus/integ/integ02/integ02.html Properties of Integrals]</ref>

<h3>Additive Distribution</h3>
If an integral contains two functions added together, it may be rewritten as two separate integrals, each containing one function.
:<math>\int_{a}^{b}(f(x)+g(x))dx=\int_{a}^{b}f(x)dx+\int_{a}^{b}g(x)dx</math>

<h3>Constant Multiplicative Distribution</h3>
If an integral contains a function multiplied by a constant, it may be rewritten as the constant times the integral of the function.
:<math>\int_{a}^{b}cf(x)dx=c\int_{a}^{b}f(x)dx</math>

<h3>Area</h3>
Any integral that contains the same upper and lower bounds is equal to zero.
:<math>\int_{a}^{a}f(x)dx=0</math>

<h3>Separation</h3>
An integral may be rewritten as the sum of two integrals with adjacent bounds.
:<math>\int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx</math>, <math>c\in(a,b)</math>

<h3>Additive Inversion</h3>
Any integral is equal to the additive inverse of the same integral with reversed upper and lower bounds.
:<math>\int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx</math>

==Antiderivative vs Integration==
There are important differences between the anti-derivative and integration. An anti-derivative of a function <math>f(x)</math> is a function <math>F(x)</math> such that,

:<math>\frac{d}{dx}F(x)=f(x)</math>

The integral of a function can be evaluated using its antiderivative,

:<math>\int_a^b f(x)dx=F(b)-F(a)</math>

This works for the kind of functions encountered in late high school and early university mathematics. It is, however, an incomplete method. For example, one cannot write the anti-derivative of <math>e^{x^{2}}</math> in terms of familiar functions (such as [[trigonometric function]]s, [[exponential]]s, and [[logarithm]]s) and function operations.

==Riemann integral==
{{main|Riemann Integral}}
As a geometric interpretation of the integral of the [[area]] under a curve, the Riemann integral consists of dividing the area under the curve of the function into slices. The [[domain]] of the function is partioned into N segments of width <math>\frac{b-a}{N}</math> The height of the segment is dependent on which side of the rectangle is taken. The lower sum takes the lower side of the rectangle, the upper sum the higher side of the rectangle. In the [[limit]] of <math>N\rightarrow\infty</math> these two [[series (mathematics)|series]] become the integral. If they approach the same value then the integral exists, otherwise it is undefined.

===Simpson's Rule===
{{Main|Simpson's rule}}
'''Simpson's Rule''' is an extension of the Riemann integral. Instead of using shapes such as rectangles or trapezoids, Simpson's Rule allows for the use of parabolas or other higher order polynomials to approximate integrals.

==Multiple integrals==
[[Image:DoubleIntegral.png|right|thumb|200px|A double integral gives the volume under a function over a given area - here, the area under the function (at top) within a square.]]

Multiple integrals are integrals extended to higher dimensions. Just like a definite integral gives the area under a 2-dimensional function, a double integral gives the volume under a three-dimensional function, and a triple integral gives the four-dimensional volume under a four-dimensional function. An ordinary integral is integrated over a single variable, such as x; similarly, a double integral is integrated over a two-dimensional area, usually written A; and a triple integral is integrated over a three-dimensional volume, usually written V.
:A double integral: <math>\iint\limits_D f(x,y) dA</math>
:A triple integral: <math>\iiint\limits_V f(x,y,z) dV</math>

[[Fubini's Theorem]] states that, for double integrals,
:<math>\iint\limits_D f(x,y) dA = \int\limits_{y_0}^{y_N} \int\limits_{x_0}^{x_N} f(x,y) dx dy</math>
and for triple integrals,
:<math>\iiint\limits_V f(x,y,z) dV = \int\limits_{z_0}^{z_N} \int\limits_{y_0}^{y_N} \int\limits_{x_0}^{x_N} f(x,y) dx dy dz</math>

These functions can be integrated with respect to the variables x, y, and z in any order. For example, the double integral above is also equivalent to <math>\int\limits_{x_0}^{x_N} \int\limits_{y_0}^{y_N} f(x,y) dy dx</math>.

==Lebesgue Integral==
The Lebesgue integral is usually introduced in late university or early postgraduate mathematics. It is naively described as rotating the Reimann integral, in that it is the range instead of the domain that is partitioned. An understanding of [[measure theory]] is required to understand this technique.

The Lebesgue integral is defined for every function for which the Riemann integral is defined, as well as for an even larger class of functions: this possibility of integrating functions which are not Riemann integrable is a large part of the motivation for the Lebesgue theory. A typical example of a function which is Lebesgue integrable but not Riemann integrable is the [[characteristic function]] of the [[rational number|rationals]], <math>\chi_{\mathbb Q}</math>, defined by
::<math>\chi_{\mathbb Q}(x) =
\begin{cases}
1 & \mbox{if } x \in \mathbb{Q}, \\
0 & \mbox{if } x \notin \mathbb{Q}
\end{cases}</math>.
Because the rationals are only countable, this function is zero "almost everywhere": there are far more irrationals than rationals, and the function is <math>0</math> at all of these. Thus we would expect that
::<math>\int_0^1 \chi_{\mathbb Q}(x) \, dx = 0</math>
Unfortunately, this function has so many discontinuities that its Riemann integral is not defined. However, if we use the Lebesgue integral instead, the function is integrable as hoped, and has the expected value <math>0</math>.

==Critisism==
Many Christians have criticised integral calculus for being sacrilegious. The reason is that the integration very closely resembles the letter ''S''. This is believed to stand for ''Satan'' and this is probably the reason why the ultra-liberals and radical leftists American Universities use integrals so often. However, some have also theorised that the ''S'' stands for ''Saint Peter'', in which case integration would be accepted among the righteous. This is still a subject of great debate among mathematicians.

==See also==
*[[Methods of integration]]
*[[Definite integral]]
*[[Indefinite integral]]
===External links===
*[http://mathworld.wolfram.com/Integral.html Integrals - Wolfram MathWorld]
*[http://www.relativitycalculator.com/mathematical_references.shtml Some Quick and Dirty Mathematical References]

==References==
{{reflist}}

[[Category:Calculus]]
[[Category:Integration]]

Methods of integration

2020-10-15T19:24:11Z

BertJonson64: new integration aspects

{{Math-h}}

This article details several methods of [[integral|integration]] for advanced high school or early university student, each with an example.

==Estimation==
There are various methods of estimating integrals. This is particularly useful if the rule for integrating is unknown or extremely complicated, as in the case of <math>e^{x^2}</math>. The primary method of estimation is the Riemann integral.

<br />Another major method, known as [[Simpson's rule]] uses the Riemann integral. Instead of using linear estimations, Simpson's rule allows for the use of [[parabola]]s or other higher order expressions to estimate integrals.
:{{main|Simpson's rule}}

==Integration by Parts==
{{main|Integration by parts}}
'''Integration by parts''' is a special technique to facilitate the integration of the product of two functions that otherwise lack an obvious integral. This technique can be proven with the [[product rule]].

The rule for '''integration by parts''' is stated as follows:
:<big><math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math></big>
:or
:<big><math>\int u\,dv = uv - \int v\,du\,</math></big>

This rule is often useful when one function is a power of ''x'' and the other function is a trigonometric function or ''e'' raised to a power of ''x''.

Note that it may be necessary to repeat the '''integration by parts''' several times, one for each power of ''x''.

==Partial Fractions==
{{Main|Partial fractions in integration}}
'''Integration by partial fractions''' is a technique to facilitate the integration of a rational expression by partial fraction decomposition.

Given an integral
<br />
:<math>\int \frac {f(x)}{g(x)}dx</math>
<br />
where <math>f(x)</math> and <math>g(x)</math> are both polynomials, integration by partial fractions shows how to separate the problem into multiple integrals before integrating.

==Algebraic Substitution==
'''Integration by Algebraic Substitution''' is a technique to facilitate the integration of a rational expression by substituting a more complicated expression with a variable.

Given an integral

:<math>\int\frac{2x}{x^2+3}dx</math>

We can substitute the term ''x''<sup>2</sup>+3 with a ''u''. Giving us

:<math>u=x^2+3</math>

We then take the derivative of ''u'' with respect to ''x'',

:<math>\frac{du}{dx}=2x</math>

We then set the terms equal to d''u'',

:<math>du=2xdx</math>

Now we are ready to rewrite the integral,

:<math>\int\frac{2x}{x^2+3}dx=\int\frac{1}{u}du</math>

We can rewrite the integral this way due to the substitution of the ''x'' terms with the ''u'' terms.

Now we can solve the integral in terms of ''u''.

:<math>\int\frac{1}{u}du=ln|u|+c</math>

Now we replace ''u'' with the term ''x''<sup>2</sup>+3 to get,

:<math>\ln|x^2+3|+c</math>

We can check this by taking the derivative of <math display="inline">\ln|x^2+3|</math>,

:<math>\frac{d}{dx}\ln|x^2+3|=\left (\frac{1}{x^2+3} \right)(2x)=\frac{2x}{x^2+3}</math>

===Reverse Chain Rule===
The reverse chain rule is a trick for integration by substitution without having to do all the steps involved with integration by substitution. It uses a reversed form of the [[chain rule]] in [[differentiation]] to integrate functions of the form f'(x)g'(f(x)), where f and g are two [[function]]s and f'(x) is the derivative of f(x). From the chain rule, which states:

:<math>
\frac{d}{dx} \left( g(f(x)) \right) = f'(x) g'(f(x))
</math>

Integrating both sides produces the reverse chain rule:

:<math>
\int f'(x) g'(f(x)) \, dx = g(f(x))
</math>

This means that if a function can be recognised in the form f'(x)g'(f(x)), then it can be integrated almost immediately. As an example, consider the function:

:<math>
y(x) = 2x \cos{\left( x^2 \right)}
</math>

Comparing to the above, f(x)=x<sup>2</sup>, f'(x)=2x and g'(x) is represented by a [[cosine]]. All wee need to do is know the integral of a cosine is [[sine]] so g(x) is sine. Therefore:

:<math>
\int 2x \cos{\left( x^2 \right)} \, dx = \sin{\left( x^2 \right)}
</math>

If the first part of the function is f'(x) multiplied by a constant, then this constant can be taken out of the integral so that it the integral is of the form f'(x)g'(f(x)). This method can also be applied to the fraction example above.

==Trigonometric Substitution==
'''Integration by Trigonometric Substitution''' is a technique to facilitate the integration of a rational expression by substituting a more complicated radical expression with a trigonometric expression. This is the least Christian technique of integration and should be avoided at all costs. Atheists invented the sine function to force conservatives learning math to write the word ''sin''.

Given an integral

:<math>\int\frac{1}{\sqrt{9-x^2}}dx</math>

By looking at the radical we can determine that it represents the base of a right triangle by understanding the [[Pythagorean theorem]].
:<math>\sqrt{9-x^2}=3+x</math>
where 3 is the hypotenuse and ''x'' is the height of the triangle.
This allows us to rewrite the expression to <math display="inline">\sin\theta=\frac{x}{3}</math>. This allows us to substitute ''x'' with <math display="inline">3\sin\theta</math>.
Now to do the substitution
:<math>9-x^2=9-(3\sin\theta )^2</math>
:<math>9-(3\sin\theta )^2=9-9\sin^2\theta </math>
:<math>9-9\sin^2\theta=9(1- \sin^2\theta) </math>
And by use of trigonometric identities we know that
:<math>1- \sin^2\theta=\cos^2\theta </math>
:<math>9(1- \sin^2\theta)=9\cos^2\theta </math>
Therefore,
:<math>\sqrt{9-x^2}=3\cos\theta </math>
We are not done yet, we must also take the derivative of <math display="inline">3\sin\theta</math>
:<math>\frac{dx}{d\theta} 3\sin\theta=3\cos\theta </math>
By partial derivatives we move the <math display="inline">d\theta</math> over.
:<math>dx=3\cos\theta d\theta </math>

Now we are ready to rewrite our integral.

:<math>\int\frac{1}{\sqrt{9-x^2}}dx=\int\frac{3\cos\theta}{3\cos\theta}d\theta=\int d\theta=\theta+c</math>

From our trigonometric expression <math display="inline">x=3\sin\theta</math> we can see that
:<math>\theta=\sin^{-1}\left(\frac{x}{3}\right)+c</math>
giving us the final solution.
:<math>\int\frac{1}{\sqrt{9-x^2}}dx=\sin^{-1}\left(\frac{x}{3}\right)+c </math>

== Other methods of integration ==
The primary methods of integration include:

* [[Integration by parts]]
* [[Integration using polar coordinates]]
* [[Multiple integration]]
* [[Residue calculus]] (for definite integrals)
* [[Method of simultaneous convolutions]]
* [[Mellin transform]]s
* [[Inflation-restriction sequence]]s

==See also==
*[[Fundamental Theorem of Calculus]]
*[[Calculus]]
*[[Integration]]
*[[Table of Indefinite Integrals]]

==External links==
*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=integral Antiderivative Solver]

[[Category:Calculus]]
[[Category:Integration]]

Roleplaying game

2020-10-15T19:05:19Z

BertJonson64: added new perspectives to the downside of RPGs

A '''roleplaying game''', or RPG, is a game where a number of participants typically assume the roles of fictional characters operating within fictional locations or an entire mythos.

One of the most popular and long running RPGs is [[Dungeons and Dragons]] which was created in the [[USA]]. It became so popular that it spawned a children's cartoon of the same name.

Traditionally, an RPG was played by a group of friends with one of the group assuming the role of "game master" and effectively running the game. These are often called "tabletop" RPGs because they employ rulebooks, pen/pencil, paper and dice of assorted shapes. Nowadays there are a great number of RPGs available in videogame format - everything from online games designed for any number of players (for example [[World of Warcraft]], [[Phantasy Star Online]], and [[Everquest]]) to single player story led games (for example, the Final Fantasy series). Proponents of tabletop RPGs criticize computer and console-based RPGs for their relative inflexibility, since even the best computer-model can't be as ingenious as an actual game-master can.

Since the 1980s, RPGs have come under a great deal of criticism from groups who feel that playing these games is inherently dangerous, especially to children, and could potentially lead to [[insanity]], [[murder]], [[suicide]], and [[occultism]].<ref>[http://www.crossroad.to/articles2/2003/occult-rpg.htm Kjos Ministries]</ref><ref>[http://theescapist.com/ The Escapist]</ref> RPGs have also been linked to an extreme [[atheistic]] world view. This is claimed because RPGs don't teach players about that all actions have [[Consequentialism|consequences]]. Many critics have also linked role-playing to unchristian and sacrilegious beliefs. This could be explained by many RPGs taking place in fictional worlds, where [[occult]] gods are worshipped.

Others have argued that RPGs can be used to teach mathematics, problem solving, social skills, and critical thinking to kids, especially those who might have trouble learning these skills in a traditional environment [http://www.theescapist.com/rwrpg/interview-rebeccathomas.htm]

== Tabletop RPGs ==
* [[Dungeons and Dragons]]
* [[Vampire: the Masquerade]]
* [[Traveller]]
* [[Top Secret]]
* [[Exalted]]
* [[Empire of the Petal Throne]]
* [[Nobilis]]
* [[Boot Hill]]
* [[In Nomine]]
* [[Dragonraid]]
* [[GURPS]]
* [[Bunnies and Burrows]]
* [[Paranoia (game)|Paranoia]]

===''Bad'' Tabletop RPGs===
Please note that the tabletop roleplaying games listed below may cause feelings of disgust or shame if for some reason you attempt to look them up online. Essentially all of these are poorly-designed and many of them feature subtly (or not-so-subtly) racist, sexist, or otherwise bigoted ideologies inherent in their ruleset or backstories.

''The "Unholy Trinity" of tabletop RPGs''
* ''[[F.A.T.A.L.]]''
* ''[[RaHoWa]]''
* ''HYBRID'' - A confusing mass of unnecessarily-complex rules with no structured backstory, HYBRID was an attempt to write rules for reality using comic books. An utter failure, both unplayable and offensive. Given the nature of the Internet, HYBRID will likely be replaced by another yet-worse RPG in time.

''Other notably-bad tabletop RPGs''
* ''Spawn of Fashan'' - one of the first "bad" RPGs, generally thought to be a deliberate parody. The game is well-optimized for people who roleplay to ruin other people's fun.
* ''The World of Synnibarr'' - Considered a terrible RPG by many online and a "B-list" RPG worth playing for the hilarity by others, the badness comes not from poor design (like virtually every other title contained herein), but from the ridiculous-by-any-standard setting. An infamous example of a typical ''Synnibarr'' monster is a flying bear with laser-beam eyes.
* ''SenZar'' - Perhaps better-designed than most of the games on this list, the balance between classes is still terribly off (even more so than the first edition of D&D). It also not only allows but openly encourages abandoning roleplaying in favor of optimizing one's character, a tack that offends many roleplayers.
* ''deadEarth'' - Ridiculed for claiming "realism" while simultaneously having comic-book-level powers gained from radiation exposure, including a table of 1000 random powers included in the core mechanics. Given backhanded praise by some critics for a rule that is often interpreted as only allowing a single player to create three characters (ever, and characters dying during the creation process is not uncommon.)
* ''Phoenix Command'' - Not so much "poorly" designed as ''over''designed, ''Phoenix Command'' and other games from the now-defunct publisher Leading Edge Games were the products of a rocket scientist attempting tabletop RPG design.
* ''Wraeththu: From Enchantment to Fulfilment'' [sic] - Almost as oversexualized as the Unholy Trinity above, ''Wraeththu'' is one of the most recent additions to the ranks of legendarily-bad RPGs, and boasts what is almost certainly the only extant depiction of an alien penis on the cover of a tabletop RPG rulebook.

==Categories==
Role Playing Games cover a wide range of activities, including counselling techniques, tabletop (aka "pen & paper") games, solo role playing, and video games.

Most Role Playing Games consist of the following components:
* Player Characters (PCs): fictional characters controlled by the player(s).
* Non-player Characters (NPCs): fictional characters controlled by the game master or computer.
* Setting: a fictional location for the PCs and NPCs. This can range from a single dungeon to an entire multiverse. Commercial settings often have involved histories, detailed important NPCs, and maps of important locations.
* Scenarios: goals for the players to accomplish. This may be a simple as killing the local dragon or travelling the world to eliminate an evil cult. Though the scenario defines the situation, the players must decide how to accomplish the goals given their PCs and their items.
* Creatures: animate creatures with which the PCs interact. This could be anything from a pet dog to a fire-breathing dragon to an android.
* Items: items that PCs interact with and/or acquire. These could be anything from the PC's clothing to magical rings to F16 fighter planes. Items acquired in one scenario are typically usable in future scenarios.
* Special effects: things not covered above that are unusual or otherwise special. This could be anything from magic spells to advanced technology.

==Tabletop Role Playing Games==
Typically tabletop role playing involves a game master (GM) and one or more players. The role of the game master is four fold: author, director, referee, and (commonly omitted) manager.

Players take on the part of one or more fictional characters. These fictional characters may be detailed by the GM or they may be created by the player, according to a set of rules defined by the game system being used. Role playing has to do with directing the fictional character in a way that is consistent with the character and the mythos in which he lives. For instance, a character in a medieval setting would have no knowledge of machine guns or lasers, even though the player does. Directing the character in a manner that is inconsistent with the foregoing may result in penalties by the GM, or may simply be ignored.

== See also ==
*[[CRPG|Console RPGs]]
*[[MMORPG]]

== References ==
<references/>

[[Category:Video Games]]

Conservapedia:Are role-playing games good for children?

2020-10-15T18:52:55Z

BertJonson64: additional arguments added

{{debate}}

==Yes==

* [[Role-playing]] games do not reinforce evil, but "get it out of your system".
* Anyway, it's just a game.
* Encourages a sense of imagination

Yes, for at least two reasons:
1) Most of the monters encountered are based on mythology and literature. Seeing the cool monsters would spark a broader interest in the classics. It did for me when I was a kid.

2) Playing those games builds problem solving skills. If you're in a party of five characters, and you're about to enter a dungeon with forty hobgoblins, you can't just walk in with swords drawn and expect to survive. To succeed at a role-playing game, you need to know how to plan, you need to find creative ways to maximize your strengths and minimize your weaknesses, you need to learn when to be aggressive and when to use caution. All of those are skills which will serve the kids well in the real world, even if (hopefully) not in the same situation.

It is true that it's bad if the child goes overboard, but that's true of anything. That's why we have parents, to keep that from happening.--[[User:Frey|Frey]] 16:04, 25 April 2008 (EDT)

'''Yes, but in moderation-''' Let them play RPGs. Most of the time they do no harm, as long as they have a stable social life, RPGs can't hurt. It's good to check the ratings, though. --[[User:TomRobinson|TomRobinson]] 13:43, 7 June 2010 (EDT)

==No==

* Acting out mental fantasies of sorcery, theft, etc., encourages these evil tendencies.

:It seems to me that "'''of course''' they are bad" is the obvious and correct conclusion. People tend to escalate in behaviors in which they indulge. When I started collecting guns, I bought one, and it was cool, so I bought a second...then my collecting got more and more pronounced. Now I actually have to budget my income to make sure I don't inadvertently indulge the hobby too much. The same goes for '''bad''' behaviors. Pedophiles, murderers, drug users, criminals, all are known to escalate over time, not start off at the top and then, the "pressure" released, revert to ordinary citizens. It's called "escalation behavior" and it's why no one, children or adults, should casually play RPGs in my opinion. Part of the reason we (meaning conservatives) seem to have, on the whole, a very relaxed attitude towards sexual and occult imagery and influences of things like [[Dungeons and Dragons]] and [[Harry Potter]] are that the influences are everywhere and we "get used to them." Though I have my issues with Catholicism, the Pope is absolutely right to refer to the "[http://www.explorefaith.org/news/08_02_05.html subtle seductions] of fictional representations of the occult. They normalize things which should be categorically condemned. Jesus Saves 19:22, 19 March 2008 (EDT)

I agree with Jesus Saves. Role-playing games corrupt the minds of children by not teaching that all actions have consequences. In a role-playing game, a player can commit murder or other crimes without ever being held responsible for that. This is similar to how an atheistic world-view has lead many to commit horrendous crimes, they do not believe that their actions on earth have any consequences. In short, role-playing games distract children from the divine consequentialism that underlies the Christian faith.

==Very Occasionally==

I think both of the Debaters above have good points. I do think it is unfair to write off all RPG's as evil. However they should be played only for enjoyment in my opinion. I would put them in same category of movies, not very profitable, but usually somewhat enjoyable. There are some interesting aspects of most of them, but not really any moral ones. However many Role Playing Games glorify Gore, Violence and suggestive content. These should be avoided, especially by children. Parents should monitor what their children play, indeed in some games such as the [[elder scrolls]] series there is a variety of dark, wicked cults for players to join. Indeed caution is required when children devote any amount of time to Role Playing Games. [[Baronvonbob]]

The Lord of the Rings

2020-10-15T08:01:10Z

BertJonson64: typos and inserted links

[[Image:Mhjfjfr7.jpg|thumb|350px|The covers for the three volumes of ''The Lord of the Rings'', designed by Tolkien.]]

'''''The Lord of the Rings''''' is a lengthy fantasy novel written by [[J.R.R. Tolkien]]. ''The Lord of the Rings'' is considered one of the most influential works of the [[fantasy]] genre in modern times.

The story of ''The Lord of the Rings'' is about the war of the peoples of [[Middle-earth]] against a Dark Lord named [[Sauron]], the eponymous "Lord of the Rings". The most powerful ring falls into the hands of a hobbit named Frodo Baggins, who is sent on a quest to destroy [[The One Ring]] deep within the enemy territory of [[Mordor]].

== Creation ==

The Lord of the Rings was published in three parts in the years 1954 and 1955, and was preceded by the prologue, ''[[The Hobbit]]''.

=== Writing ===
After the success of his earlier book ''[[The Hobbit]]'', Tolkien's publishers persuaded him to write a sequel. He began writing in December 1937, but the first drafts were still far away from the finished version. After writing and re-writing the beginning several times, Tolkien realized the role of the [[One Ring (Middle-earth)|One Ring]] and the quest it entailed in the spring of 1938, while writing the discussion between Gildor Inglorion and the later [[Frodo Baggins]]. This was the point upon which the back story and central quest that would be ''The Lord of the Rings'' came together in his mind. It was also the point that he firmly set the book's plot into his already existing [[Middle-earth]] legendarium. Whereas the ''The Hobbit'' had before been separate from his Middle-earth mythology, while still borrowing ideas, names, and persons from it, Tolkien now consciously moved it and its sequel into the Middle-earth setting. This resulted in the changes in tone, and in the meaning of formerly unimportant things as the 'magic ring' and the Necromancer, who both gained literary importance in the sequel. While the ''The Hobbit'' was written as a story intended for his children, ''The Lord of the Rings'' due to the realization of the later plot, soon became an epic tale of much greater proportions, both in plot and in length.

The earlier drafts and versions of ''The Lord of the Rings'' were published posthumously by his son Christopher Tolkien in ''The History of The Lord of the Rings'' (1988-1992), which are volumes VI–IX of ''The History of Middle-earth''.

In the story of the Middle-earth legendarium, ''The Hobbit'' appears as Bilbo's story of his journey and the finding of the Ring, while ''The Lord of the Rings'' are Frodo's later additions of the War of the Ring, both of which form the ''[[Red Book of Westmarch]]''.

=== Publication ===
Although often wrongly thought to be a [[trilogy]], ''The Lord of the Rings'' was conceived by the author as a single work. Its internal structure divides it into six 'books', named Book I-VI, according to the plot, with several appendices and an index. Because of paper shortages, the amount of paper needed and to reduce financial risk, it was released by the publisher [[Allen & Unwin]] in three volumes, each containing two Books:
#''[[The Fellowship of the Ring]]''
#''[[The Two Towers]]''
#''[[The Return of the King]]''
This resulted in the common error of calling ''The Lord of the Rings'' a [[trilogy]], a term which Tolkien rejected, just as he disliked the book being published in separate volumes. The first two volumes were published in 1954, and the third in 1955. It was initially published in hardbound.

In 1965 an American paperback publisher released a "pirated" paperback edition, paying Tolkien nothing, in the belief that Tolkien's copyright in the U. S. was defective because of a technicality. Tolkien reached a legal settlement with this publisher, and another publisher released an authorized edition for which Tolkien was paid royalties. The book was an instant success, particularly among college students.

== Story ==
=== Background story ===
In the [[Second Age (Middle-earth)|Second Age]] the Dark Lord [[Sauron]] created the [[One Ring (Middle-earth)|One Ring]] to help him conquer the peoples of Middle-earth. The [[Quendi|Elves]] and [[Man (Middle-earth)|Men]] of Middle-earth, led by High King Gil-galad of the [[Noldor]] and King Elendil of the [[Arnor|Dúnedain]], formed the ''[[Last Alliance of Elves and Men]]'' to fight him. Sauron was defeated and the Ring cut from his hand, thus the ''[[War of the Last Alliance]]'' ended, beginning the [[Third Age (Middle-earth)|Third Age]].

The story takes place at a time when the Elves, immortal and fairest of all beings in the world, are leaving the war-weary world to sail to the blessed realm of [[Valinor]]. With the departure of the Elves, the Age of Men has come. But the Dark Lord [[Sauron]], not truly killed at the end of the last Age, has been regaining power over the millennia since his defeat. Instrumental in his survival was the [[One Ring (Middle-earth)|One Ring]], which had kept him alive, and for which he now searches. This Ring, which had been lost for millennia, fell by chance into the hands of the [[hobbit]] [[Bilbo Baggins]], the story of which is told in ''[[The Hobbit]]''. At the beginning of ''The Lord of the Rings'', sixty years have passed since Bilbo found the One Ring.

=== The Fellowship of the Ring ===
==== Book I ====
The [[Hobbit]] [[Bilbo Baggins]] celebrates his 111th birthday, after which he leaves [[Shire (Middle-earth)|the Shire]] to travel once more, leaving his home Bag End and his [[One Ring (Middle-earth)|magic ring]] to his heir [[Frodo Baggins|Frodo]].

In [[Middle-earth chronology|T.A.]] 3018, Frodo is visited by his old friend, the Wizard [[Gandalf]], who tells him of the Ring's history and gives him the task of taking the Ring to the [[Quendi|Elven]] refuge [[Rivendell]]. Frodo leaves the Shire joined by his friends [[Samwise Gamgee|Sam Gamgee]], [[Meriadoc Brandybuck|Merry Brandybuck]], and [[Peregrin Took|Pippin Took]], all the while pursued by the mysterious otherworldly [[Nazgûl|Black Riders]], servants of Sauron. After an adventurous time they arrive in [[Breeland|Bree]], where they meet the human Ranger [[Aragorn|Strider]]. With his help they manage the make the last stretch of the way to the Ford of [[Bruinen]] at Rivendell.

==== Book II ====
The group have made it to [[Rivendell]], where the Council of Elrond decides over further action. The Ring shall be destroyed, which can only be done in [[Mount Doom]] in Sauron's land [[Mordor]] where it was forged. A group of companions are chosen to accompany Frodo on his quest, forming the Fellowship of the Ring: the hobbits Frodo, Sam, Merry, and Pippin, the Wizard [[Gandalf|Gandalf the Grey]], [[Gimli son of Glóin|Gimli]] the Dwarf, [[Legolas]] the Elf, and the Men [[Boromir]] of [[Gondor]] and [[Aragorn|Aragorn of the Dúnedain]]. The Fellowship journeys south, and after failing to cross the [[Misty Mountains]], goes under them through the Dwarven [[Khazad-dûm|Mines of Moria]]. There they are attacked by Orcs and lose their leader Gandalf to the [[Balrog]]. The Fellowship rest in the Elven realm [[Lothlórien]], and continue by boat down the river [[Anduin]]. At the Falls of Rauros they rest again, and Boromir tries unsuccessfully to take the Ring from Frodo. While the Fellowship searches for him, Frodo secretly leaves them behind to continue his quest all by himself, but Sam catches up with him and joins him on his way to Mordor.

=== The Two Towers ===
==== Book III ====
Boromir is mortally wounded defending Merry and Pippin from Orcs. Aragorn, Legolas, and Gimli decide to follow the Orcs into [[Rohan (Middle-earth)|Rohan]] to rescue the kidnapped hobbits. Merry and Pippin manage to escape [[Saruman]]'s Orcs at [[Fangorn|Fangorn Forest]], where they meet [[Treebeard]] the Ent. The tree-like Ents hold council, and decide to attack Saruman at [[Isengard]]. In Fangorn Forest Aragorn, Legolas, and Gimli meet the returned Gandalf the White, who takes them to the capital [[Edoras]], where they join [[Théoden|King Théoden of Rohan]] in the fight against Saruman. The forces of Rohan prevail against Saruman's armies in the ''Battle of the [[Helm's Deep|Hornburg]]''. Afterwards they go to Isengard to confront Saruman, whom is cast out of the Order by Gandalf. Pippin picks up the ''[[palantír]]'', and alerts Sauron to their presence. Gandalf and Pippin set of for [[Gondor]].

==== Book IV ====
Back in the Emyn Muil, Frodo and Sam journey east towards Mordor, trailed by [[Gollum]]. They capture him and he promises to lead them on their way. They travel though the Dead Marshes to the [[Morannon|Black Gate]], where Gollum leads them south. In [[Ithilien]] they are captured by [[Faramir]] of Gondor, but he releases them after hearing about their quest. Gollum leads them to and abandons them at the Pass of [[Cirith Ungol]], where they are attacked by the giant spider Shelob. Assuming Frodo dead, Sam takes the Ring to finish the quest on his own. Frodo's body is taken by a patrol of Orcs, who reveal that Frodo is only paralyzed. Sam, who has secretly followed them, tries to rescue Frodo, but is late and locked out of the Tower of Cirith Ungol.

=== The Return of the King ===
==== Book V ====
Gandalf and Pippin arrive in the city of [[Minas Tirith]], where they meet [[Denethor|Steward Denethor II]] of Gondor, and Pippin enters his service. Aragorn and his companions are joined by a group of Rangers from Rivendell. They go through the [[Ered Nimrais|Paths of the Dead]] and Aragorn summons the Dead Men of Dunharrow to his aid, and then rides east. King Théoden is summoned to Gondor, and the Rohirrim and Merry ride to Minas Tirith. Minas Tirith is besieged by the Sauron's armies. The following ''Battle of the [[Pelennor Fields]]'' is won with the help of the Rohirrim and the arrival of Aragorn with reinforcements from the southern regions of Gondor. Théoden is killed, but Éowyn and Merry slay the [[Witch-king of Angmar]]. Aragorn leads the combined forces of the West against Sauron in a move to distract him from Frodo, resulting in the ''Battle of the [[Morannon|Black Gate]]''.

==== Book VI ====
Sam rescues Frodo and returns the Ring to him. They continue the trek across Mordor. At Mount Doom they are attacked by Gollum. Frodo succumbs to the power of the Ring, claims it as his own and puts it on. Gollum fights him, biting off his finger and taking the Ring, but slips and falls into the [[Sammath Naur|Cracks of Doom]], destroying the Ring. Sauron is defeated and his power crumbles. The ''Battle of the Black Gate'' is won, and Gandalf sends the Eagles to rescue Frodo and Sam. Aragorn becomes King of Arnor and Gondor. Everyone returns homeward, and the hobbits return to [[Shire (Middle-earth)|the Shire]]. The land has been taken over by Saruman and his men, but after the ''Scouring of the Shire'' led by the returned hobbits, Saruman is killed and the hobbits can begin reordering their land. After a few years Frodo, who has been greatly hurt and burdenend though his quest and the Ring, traveled to the [[Mithlond|Grey Havens]]. There he bids his hobbit-friends good-bye, and leaves together with Bilbo, Gandalf, Elrond and Galadriel for the Undying Lands in the West, ending the [[Third Age (Middle-earth)|Third Age]] of Middle-earth. Sam, Merry and Pippin return to the Shire and their homes.

=== Appendices ===
''The Lord of the Rings'' is followed by six appendices, which give more background and detail on the history, peoples, languages, and various other topics of Middle-earth.
* '''Appendix A Annals of the Kings and Rulers''': contains further information on the history of [[Númenor]], [[Arnor]] and [[Gondor]], and of the [[Lôgrad|Rohirrim]] and [[Durin's Folk]].
* '''Appendix B The Tale of Years (Chronology of the Westlands)''': contains the timeline and chronicles of the [[Middle-earth chronology|Ages]].
* '''Appendix D Calendars''': the different [[Middle-earth chronology|calendar systems]].
* '''Appendix E Writing and Spelling''': on the pronunciation and the [[Tolkien's scripts|scripts]].
* '''Appendix F''': overview of the [[Tolkien's languages|languages]], and notes on the fictional "translation" of the book from the [[Westron]] language.

== Reception ==
From the beginning, ''The Lord of the Rings'' has received very mixed reviews, which range from high praise to condemnation. ''The Lord of the Rings'' has been considered one of the most influential works on the modern time [[fantasy]] genre.

In 1965, a US-American pirated paperback edition and the surrounding trouble spread awareness of ''The Lord of the Rings'' in the United States, where it soon gained a strong following.

Many times people have tried to interpret ''The Lord of the Rings'' as an [[allegory]]. Tolkien himself renounced that claim, stating he disliked allegory and that the ''The Lord of the Rings'' was not an allegory, which he also explained in the foreword to the book's second edition. Instead of being allegorical, he said that the book had a quality he called "applicability": because it was a story about universal themes and struggles, it could be likened to almost any situation in real life.<ref>"As for any inner meaning or 'message', it has in the intention of the author none. It is neither allegorical nor topical. [...] The real war does not resemble the legendary war in its process or its conclusion. [...] Other arrangements could be devised according to the tastes or views of those who like allegory or topical reference. But I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history, true or feigned, with its varied applicability to the thought and experience of readers. I think that many confuse 'applicability' with 'allegory'; but the one resides in the freedom of the reader, and the other in the purposed domination of the author.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref> This universality would result in it often being interpreted as an allegory, sometimes ironically from opposing ideological sides. For instance, J. R. R. Tolkien was a [[Roman Catholic]], and despite his statements that ''The Lord of the Rings'' was not an allegory some readers have seen [[Christian]] undertones in ''The Lord of the Rings.'' <ref>"Much as it is possible to identify allegories of the Second World war into ''The Lord of the Rings'', it is possible to identify any number of Christian allegories as well" in Smith, J. and Matthews, J.C. ''The Lord of the Rings: the Films, the books, the radio series'' (Virgin Books 2004), p.116.</ref> Tolkien himself specifically discounted the belief that he wrote the book as a direct Christian allegory—or any other sort of allegory, which he went on record as "cordially disliking" and saw as besides the point of good storytelling in the medieval sense, and preferring "applicability"—in contrast with the overt and acknowledged allegories in the works of Tolkien's friend, [[C. S. Lewis]].<ref>''The Letters of J. R. R. Tolkien'', #129</ref>

Tolkien's scarring experiences in [[World War I]] and his distaste for destructive industrialism - seen in the books in his characterization of [[Saruman]]'s armies - has been an influence on his works, as acknowledged by himself.<ref>"An author cannot, of course, remain wholly unaffected by his experience [...] One has indeed personally to come under the shadow of war to feel fully its oppression; but as the years go by it seems now often forgotten that to be caught in youth by 1914 was no less hideous an experience than to be involved in 1939 and the following years. [...] It has indeed some basis in experience, though slender (for the economic situation was entirely different), and much further back. The country in which I lived in childhood was being shabbily destroyed before I was ten, in days when motor-cars were rare objects (I had never seen one) and men were still building suburban railways. Recently I saw in a paper a picture of the last decrepitude of the once thriving corn-mill beside its pool that long ago seemed to me so important.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref><ref>John Garth, "Tolkien and the Great War: The Threshold of Middle Earth," available at [https://www.amazon.com/Tolkien-Great-War-Threshold-Middle-earth/dp/0618331298 Amazon.com].</ref> However, Tolkien did state that "The Lord of the Rings is, of course, a fundamentally religious and Catholic work; unconsciously so at first, but consciously in the revision[]"—which indicates his devoted faith.<ref>[https://www.grin.com/document/22410]</ref>

Many have criticised Tolkien's adaptation of [[Eowyn]] in the third book: ''The Return of The King''. The fact that she is feautered in combat is generally considered to be anti-conservative. The fact that the military should be reserved for men has also been endorsed by vice-president [[Mike Pence]]. Due to this, Swedish translator Åke Ohlmarks later edited the chapter: ''The Battle of Pelennor Fields'' so that [[Merry Brandybuck]] was the one who killed the which-king, rather than Eowyn. Ohlmarks said that the edit was closer to Tolkiens original vision and claimed that Tolkien might have intended it to be Merry who killed the which king all along. The original text: 'Then tottering, struggling up, with her last strength she drove her sword between crown and mantle, as the great shoulders bowed before her.' is believed to be a typo where Tolkien intended to have ''him'' instead of ''her''. This was corrected by Ohlmarks in the Swedish translation of the book.

== Sequel ==

Tolkien attempted to write a sequel to ''The Lord of the Rings''. Although he did a first draft, he would never complete it. The unfinished work is now part of the 12th volume of ''The History of Middle-earth'', under the title of ''The New Shadow''.

== Adaptions ==
''The Lord of the Rings'' has been adapted full or in part in a variety of media. Among these are films, stage plays and a musical.

=== The Lord of the Rings film trilogy ===
'''''The Lord of the Rings'' film trilogy''' were three films based on the book, all directed by [[Peter Jackson]], produced by [[New Line Cinema]] and filmed in [[New Zealand]]. The film titles were derived from the three volumes:

* ''[[The Fellowship of the Ring (film, 2001)|The Lord of the Rings: The Fellowship of the Ring]]'' (2001)
* ''[[The Two Towers (film, 2002)|The Lord of the Rings: The Two Towers]]'' (2002)
* ''[[The Return of the King (film, 2003)|The Lord of the Rings: The Return of the King]]'' (2003)

The films were released annually in cinemas from December 2001 to 2003. DVD releases of the cinema version and Special Extended Editions have also been released for each film. Each extended edition includes four discs, two of bonus material.

The Lord of the Rings film trilogy received universal acclaim from critics and fans alike. Some even cited it as "the [[Star Wars]] Trilogy for [[Millennials]]". The trilogy had 30 [[Academy Awards|Oscar]] nominations, 17 of which it won. One of them being Best Picture, which was won by ''The Return of the King'' at the 76th Academy Awards in 2004. ''The Return of the King'' is also the only film in cinematic history that won every Oscar it was nominated for, 11 in all. It is tied with ''[[Titanic (1997 film)|Titanic]]'' and ''[[Ben-Hur (1959 film)|Ben-Hur]]'' as the film that won the most Academy Awards in cinematic history.<ref>[http://www.filmsite.org/oscars2.html#1]</ref> Both the first and third films in the series also won [[Movieguide]]'s "Best Movie for Mature Audiences" award in 2002 and 2004, respectively.<ref>[https://movieguideawards.com/category/winners/]</ref>

== References ==
{{reflist|2}}

== See also ==
*''[[The Hobbit]]''

{{Middle-earth}}
{{DEFAULTSORT:Lord of the Rings, The}}
[[Category:Middle-earth]]
[[Category:Lord of the Rings| ]]
[[Category:Novels]]
[[Category:Greatest Conservative Novels]]

The Lord of the Rings

2020-10-15T07:53:11Z

BertJonson64: typo

[[Image:Mhjfjfr7.jpg|thumb|350px|The covers for the three volumes of ''The Lord of the Rings'', designed by Tolkien.]]

'''''The Lord of the Rings''''' is a lengthy fantasy novel written by [[J.R.R. Tolkien]]. ''The Lord of the Rings'' is considered one of the most influential works of the [[fantasy]] genre in modern times.

The story of ''The Lord of the Rings'' is about the war of the peoples of [[Middle-earth]] against a Dark Lord named [[Sauron]], the eponymous "Lord of the Rings". The most powerful ring falls into the hands of a hobbit named Frodo Baggins, who is sent on a quest to destroy [[The One Ring]] deep within the enemy territory of [[Mordor]].

== Creation ==

The Lord of the Rings was published in three parts in the years 1954 and 1955, and was preceded by the prologue, ''[[The Hobbit]]''.

=== Writing ===
After the success of his earlier book ''[[The Hobbit]]'', Tolkien's publishers persuaded him to write a sequel. He began writing in December 1937, but the first drafts were still far away from the finished version. After writing and re-writing the beginning several times, Tolkien realized the role of the [[One Ring (Middle-earth)|One Ring]] and the quest it entailed in the spring of 1938, while writing the discussion between Gildor Inglorion and the later [[Frodo Baggins]]. This was the point upon which the back story and central quest that would be ''The Lord of the Rings'' came together in his mind. It was also the point that he firmly set the book's plot into his already existing [[Middle-earth]] legendarium. Whereas the ''The Hobbit'' had before been separate from his Middle-earth mythology, while still borrowing ideas, names, and persons from it, Tolkien now consciously moved it and its sequel into the Middle-earth setting. This resulted in the changes in tone, and in the meaning of formerly unimportant things as the 'magic ring' and the Necromancer, who both gained literary importance in the sequel. While the ''The Hobbit'' was written as a story intended for his children, ''The Lord of the Rings'' due to the realization of the later plot, soon became an epic tale of much greater proportions, both in plot and in length.

The earlier drafts and versions of ''The Lord of the Rings'' were published posthumously by his son Christopher Tolkien in ''The History of The Lord of the Rings'' (1988-1992), which are volumes VI–IX of ''The History of Middle-earth''.

In the story of the Middle-earth legendarium, ''The Hobbit'' appears as Bilbo's story of his journey and the finding of the Ring, while ''The Lord of the Rings'' are Frodo's later additions of the War of the Ring, both of which form the ''[[Red Book of Westmarch]]''.

=== Publication ===
Although often wrongly thought to be a [[trilogy]], ''The Lord of the Rings'' was conceived by the author as a single work. Its internal structure divides it into six 'books', named Book I-VI, according to the plot, with several appendices and an index. Because of paper shortages, the amount of paper needed and to reduce financial risk, it was released by the publisher [[Allen & Unwin]] in three volumes, each containing two Books:
#''[[The Fellowship of the Ring]]''
#''[[The Two Towers]]''
#''[[The Return of the King]]''
This resulted in the common error of calling ''The Lord of the Rings'' a [[trilogy]], a term which Tolkien rejected, just as he disliked the book being published in separate volumes. The first two volumes were published in 1954, and the third in 1955. It was initially published in hardbound.

In 1965 an American paperback publisher released a "pirated" paperback edition, paying Tolkien nothing, in the belief that Tolkien's copyright in the U. S. was defective because of a technicality. Tolkien reached a legal settlement with this publisher, and another publisher released an authorized edition for which Tolkien was paid royalties. The book was an instant success, particularly among college students.

== Story ==
=== Background story ===
In the [[Second Age (Middle-earth)|Second Age]] the Dark Lord [[Sauron]] created the [[One Ring (Middle-earth)|One Ring]] to help him conquer the peoples of Middle-earth. The [[Quendi|Elves]] and [[Man (Middle-earth)|Men]] of Middle-earth, led by High King Gil-galad of the [[Noldor]] and King Elendil of the [[Arnor|Dúnedain]], formed the ''[[Last Alliance of Elves and Men]]'' to fight him. Sauron was defeated and the Ring cut from his hand, thus the ''[[War of the Last Alliance]]'' ended, beginning the [[Third Age (Middle-earth)|Third Age]].

The story takes place at a time when the Elves, immortal and fairest of all beings in the world, are leaving the war-weary world to sail to the blessed realm of [[Valinor]]. With the departure of the Elves, the Age of Men has come. But the Dark Lord [[Sauron]], not truly killed at the end of the last Age, has been regaining power over the millennia since his defeat. Instrumental in his survival was the [[One Ring (Middle-earth)|One Ring]], which had kept him alive, and for which he now searches. This Ring, which had been lost for millennia, fell by chance into the hands of the [[hobbit]] [[Bilbo Baggins]], the story of which is told in ''[[The Hobbit]]''. At the beginning of ''The Lord of the Rings'', sixty years have passed since Bilbo found the One Ring.

=== The Fellowship of the Ring ===
==== Book I ====
The [[Hobbit]] [[Bilbo Baggins]] celebrates his 111th birthday, after which he leaves [[Shire (Middle-earth)|the Shire]] to travel once more, leaving his home Bag End and his [[One Ring (Middle-earth)|magic ring]] to his heir [[Frodo Baggins|Frodo]].

In [[Middle-earth chronology|T.A.]] 3018, Frodo is visited by his old friend, the Wizard [[Gandalf]], who tells him of the Ring's history and gives him the task of taking the Ring to the [[Quendi|Elven]] refuge [[Rivendell]]. Frodo leaves the Shire joined by his friends [[Samwise Gamgee|Sam Gamgee]], [[Meriadoc Brandybuck|Merry Brandybuck]], and [[Peregrin Took|Pippin Took]], all the while pursued by the mysterious otherworldly [[Nazgûl|Black Riders]], servants of Sauron. After an adventurous time they arrive in [[Breeland|Bree]], where they meet the human Ranger [[Aragorn|Strider]]. With his help they manage the make the last stretch of the way to the Ford of [[Bruinen]] at Rivendell.

==== Book II ====
The group have made it to [[Rivendell]], where the Council of Elrond decides over further action. The Ring shall be destroyed, which can only be done in [[Mount Doom]] in Sauron's land [[Mordor]] where it was forged. A group of companions are chosen to accompany Frodo on his quest, forming the Fellowship of the Ring: the hobbits Frodo, Sam, Merry, and Pippin, the Wizard [[Gandalf|Gandalf the Grey]], [[Gimli son of Glóin|Gimli]] the Dwarf, [[Legolas]] the Elf, and the Men [[Boromir]] of [[Gondor]] and [[Aragorn|Aragorn of the Dúnedain]]. The Fellowship journeys south, and after failing to cross the [[Misty Mountains]], goes under them through the Dwarven [[Khazad-dûm|Mines of Moria]]. There they are attacked by Orcs and lose their leader Gandalf to the [[Balrog]]. The Fellowship rest in the Elven realm [[Lothlórien]], and continue by boat down the river [[Anduin]]. At the Falls of Rauros they rest again, and Boromir tries unsuccessfully to take the Ring from Frodo. While the Fellowship searches for him, Frodo secretly leaves them behind to continue his quest all by himself, but Sam catches up with him and joins him on his way to Mordor.

=== The Two Towers ===
==== Book III ====
Boromir is mortally wounded defending Merry and Pippin from Orcs. Aragorn, Legolas, and Gimli decide to follow the Orcs into [[Rohan (Middle-earth)|Rohan]] to rescue the kidnapped hobbits. Merry and Pippin manage to escape [[Saruman]]'s Orcs at [[Fangorn|Fangorn Forest]], where they meet [[Treebeard]] the Ent. The tree-like Ents hold council, and decide to attack Saruman at [[Isengard]]. In Fangorn Forest Aragorn, Legolas, and Gimli meet the returned Gandalf the White, who takes them to the capital [[Edoras]], where they join [[Théoden|King Théoden of Rohan]] in the fight against Saruman. The forces of Rohan prevail against Saruman's armies in the ''Battle of the [[Helm's Deep|Hornburg]]''. Afterwards they go to Isengard to confront Saruman, whom is cast out of the Order by Gandalf. Pippin picks up the ''[[palantír]]'', and alerts Sauron to their presence. Gandalf and Pippin set of for [[Gondor]].

==== Book IV ====
Back in the Emyn Muil, Frodo and Sam journey east towards Mordor, trailed by [[Gollum]]. They capture him and he promises to lead them on their way. They travel though the Dead Marshes to the [[Morannon|Black Gate]], where Gollum leads them south. In [[Ithilien]] they are captured by [[Faramir]] of Gondor, but he releases them after hearing about their quest. Gollum leads them to and abandons them at the Pass of [[Cirith Ungol]], where they are attacked by the giant spider Shelob. Assuming Frodo dead, Sam takes the Ring to finish the quest on his own. Frodo's body is taken by a patrol of Orcs, who reveal that Frodo is only paralyzed. Sam, who has secretly followed them, tries to rescue Frodo, but is late and locked out of the Tower of Cirith Ungol.

=== The Return of the King ===
==== Book V ====
Gandalf and Pippin arrive in the city of [[Minas Tirith]], where they meet [[Denethor|Steward Denethor II]] of Gondor, and Pippin enters his service. Aragorn and his companions are joined by a group of Rangers from Rivendell. They go through the [[Ered Nimrais|Paths of the Dead]] and Aragorn summons the Dead Men of Dunharrow to his aid, and then rides east. King Théoden is summoned to Gondor, and the Rohirrim and Merry ride to Minas Tirith. Minas Tirith is besieged by the Sauron's armies. The following ''Battle of the [[Pelennor Fields]]'' is won with the help of the Rohirrim and the arrival of Aragorn with reinforcements from the southern regions of Gondor. Théoden is killed, but Éowyn and Merry slay the [[Witch-king of Angmar]]. Aragorn leads the combined forces of the West against Sauron in a move to distract him from Frodo, resulting in the ''Battle of the [[Morannon|Black Gate]]''.

==== Book VI ====
Sam rescues Frodo and returns the Ring to him. They continue the trek across Mordor. At Mount Doom they are attacked by Gollum. Frodo succumbs to the power of the Ring, claims it as his own and puts it on. Gollum fights him, biting off his finger and taking the Ring, but slips and falls into the [[Sammath Naur|Cracks of Doom]], destroying the Ring. Sauron is defeated and his power crumbles. The ''Battle of the Black Gate'' is won, and Gandalf sends the Eagles to rescue Frodo and Sam. Aragorn becomes King of Arnor and Gondor. Everyone returns homeward, and the hobbits return to [[Shire (Middle-earth)|the Shire]]. The land has been taken over by Saruman and his men, but after the ''Scouring of the Shire'' led by the returned hobbits, Saruman is killed and the hobbits can begin reordering their land. After a few years Frodo, who has been greatly hurt and burdenend though his quest and the Ring, traveled to the [[Mithlond|Grey Havens]]. There he bids his hobbit-friends good-bye, and leaves together with Bilbo, Gandalf, Elrond and Galadriel for the Undying Lands in the West, ending the [[Third Age (Middle-earth)|Third Age]] of Middle-earth. Sam, Merry and Pippin return to the Shire and their homes.

=== Appendices ===
''The Lord of the Rings'' is followed by six appendices, which give more background and detail on the history, peoples, languages, and various other topics of Middle-earth.
* '''Appendix A Annals of the Kings and Rulers''': contains further information on the history of [[Númenor]], [[Arnor]] and [[Gondor]], and of the [[Lôgrad|Rohirrim]] and [[Durin's Folk]].
* '''Appendix B The Tale of Years (Chronology of the Westlands)''': contains the timeline and chronicles of the [[Middle-earth chronology|Ages]].
* '''Appendix D Calendars''': the different [[Middle-earth chronology|calendar systems]].
* '''Appendix E Writing and Spelling''': on the pronunciation and the [[Tolkien's scripts|scripts]].
* '''Appendix F''': overview of the [[Tolkien's languages|languages]], and notes on the fictional "translation" of the book from the [[Westron]] language.

== Reception ==
From the beginning, ''The Lord of the Rings'' has received very mixed reviews, which range from high praise to condemnation. ''The Lord of the Rings'' has been considered one of the most influential works on the modern time [[fantasy]] genre.

In 1965, a US-American pirated paperback edition and the surrounding trouble spread awareness of ''The Lord of the Rings'' in the United States, where it soon gained a strong following.

Many times people have tried to interpret ''The Lord of the Rings'' as an [[allegory]]. Tolkien himself renounced that claim, stating he disliked allegory and that the ''The Lord of the Rings'' was not an allegory, which he also explained in the foreword to the book's second edition. Instead of being allegorical, he said that the book had a quality he called "applicability": because it was a story about universal themes and struggles, it could be likened to almost any situation in real life.<ref>"As for any inner meaning or 'message', it has in the intention of the author none. It is neither allegorical nor topical. [...] The real war does not resemble the legendary war in its process or its conclusion. [...] Other arrangements could be devised according to the tastes or views of those who like allegory or topical reference. But I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history, true or feigned, with its varied applicability to the thought and experience of readers. I think that many confuse 'applicability' with 'allegory'; but the one resides in the freedom of the reader, and the other in the purposed domination of the author.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref> This universality would result in it often being interpreted as an allegory, sometimes ironically from opposing ideological sides. For instance, J. R. R. Tolkien was a [[Roman Catholic]], and despite his statements that ''The Lord of the Rings'' was not an allegory some readers have seen [[Christian]] undertones in ''The Lord of the Rings.'' <ref>"Much as it is possible to identify allegories of the Second World war into ''The Lord of the Rings'', it is possible to identify any number of Christian allegories as well" in Smith, J. and Matthews, J.C. ''The Lord of the Rings: the Films, the books, the radio series'' (Virgin Books 2004), p.116.</ref> Tolkien himself specifically discounted the belief that he wrote the book as a direct Christian allegory—or any other sort of allegory, which he went on record as "cordially disliking" and saw as besides the point of good storytelling in the medieval sense, and preferring "applicability"—in contrast with the overt and acknowledged allegories in the works of Tolkien's friend, [[C. S. Lewis]].<ref>''The Letters of J. R. R. Tolkien'', #129</ref>

Tolkien's scarring experiences in [[World War I]] and his distaste for destructive industrialism - seen in the books in his characterization of [[Saruman]]'s armies - has been an influence on his works, as acknowledged by himself.<ref>"An author cannot, of course, remain wholly unaffected by his experience [...] One has indeed personally to come under the shadow of war to feel fully its oppression; but as the years go by it seems now often forgotten that to be caught in youth by 1914 was no less hideous an experience than to be involved in 1939 and the following years. [...] It has indeed some basis in experience, though slender (for the economic situation was entirely different), and much further back. The country in which I lived in childhood was being shabbily destroyed before I was ten, in days when motor-cars were rare objects (I had never seen one) and men were still building suburban railways. Recently I saw in a paper a picture of the last decrepitude of the once thriving corn-mill beside its pool that long ago seemed to me so important.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref><ref>John Garth, "Tolkien and the Great War: The Threshold of Middle Earth," available at [https://www.amazon.com/Tolkien-Great-War-Threshold-Middle-earth/dp/0618331298 Amazon.com].</ref> However, Tolkien did state that "The Lord of the Rings is, of course, a fundamentally religious and Catholic work; unconsciously so at first, but consciously in the revision[]"—which indicates his devoted faith.<ref>[https://www.grin.com/document/22410]</ref>

Many have criticised Tolkien's adaptation of Eowyn in the third book: ''The Return of The King''. The fact that she is feautered in combat is generally considered to be anti-conservative. The fact that the military should be reserved for men has also been endorsed by vice-president Mike Pence. Due to this, Swedish translator Åke Ohlmark later edited the chapter: ''The Battle of Pelennor Fields'' so that Merry Brandybuck was the one who killed the which-king, rather than Eowyn. Åhlmark said that the edit was closer to Tolkiens original vision and claimed that Tolkien might have intended it to be Merry who milled the which king all along. The original text: 'Then tottering, struggling up, with her last strength she drove her sword between crown and mantle, as the great shoulders bowed before her.' is believed to be a typo where Tolkien intended to have ''him'' instead of ''her''. This was corrected by Åhlmark in the Swedish translation of the book.

== Sequel ==

Tolkien attempted to write a sequel to ''The Lord of the Rings''. Although he did a first draft, he would never complete it. The unfinished work is now part of the 12th volume of ''The History of Middle-earth'', under the title of ''The New Shadow''.

== Adaptions ==
''The Lord of the Rings'' has been adapted full or in part in a variety of media. Among these are films, stage plays and a musical.

=== The Lord of the Rings film trilogy ===
'''''The Lord of the Rings'' film trilogy''' were three films based on the book, all directed by [[Peter Jackson]], produced by [[New Line Cinema]] and filmed in [[New Zealand]]. The film titles were derived from the three volumes:

* ''[[The Fellowship of the Ring (film, 2001)|The Lord of the Rings: The Fellowship of the Ring]]'' (2001)
* ''[[The Two Towers (film, 2002)|The Lord of the Rings: The Two Towers]]'' (2002)
* ''[[The Return of the King (film, 2003)|The Lord of the Rings: The Return of the King]]'' (2003)

The films were released annually in cinemas from December 2001 to 2003. DVD releases of the cinema version and Special Extended Editions have also been released for each film. Each extended edition includes four discs, two of bonus material.

The Lord of the Rings film trilogy received universal acclaim from critics and fans alike. Some even cited it as "the [[Star Wars]] Trilogy for [[Millennials]]". The trilogy had 30 [[Academy Awards|Oscar]] nominations, 17 of which it won. One of them being Best Picture, which was won by ''The Return of the King'' at the 76th Academy Awards in 2004. ''The Return of the King'' is also the only film in cinematic history that won every Oscar it was nominated for, 11 in all. It is tied with ''[[Titanic (1997 film)|Titanic]]'' and ''[[Ben-Hur (1959 film)|Ben-Hur]]'' as the film that won the most Academy Awards in cinematic history.<ref>[http://www.filmsite.org/oscars2.html#1]</ref> Both the first and third films in the series also won [[Movieguide]]'s "Best Movie for Mature Audiences" award in 2002 and 2004, respectively.<ref>[https://movieguideawards.com/category/winners/]</ref>

== References ==
{{reflist|2}}

== See also ==
*''[[The Hobbit]]''

{{Middle-earth}}
{{DEFAULTSORT:Lord of the Rings, The}}
[[Category:Middle-earth]]
[[Category:Lord of the Rings| ]]
[[Category:Novels]]
[[Category:Greatest Conservative Novels]]

The Lord of the Rings

2020-10-15T07:50:54Z

BertJonson64: corrected some typos and added additional information

[[Image:Mhjfjfr7.jpg|thumb|350px|The covers for the three volumes of ''The Lord of the Rings'', designed by Tolkien.]]

'''''The Lord of the Rings''''' is a lengthy fantasy novel written by [[J.R.R. Tolkien]]. ''The Lord of the Rings'' is considered one of the most influential works of the [[fantasy]] genre in modern times.

The story of ''The Lord of the Rings'' is about the war of the peoples of [[Middle-earth]] against a Dark Lord named [[Sauron]], the eponymous "Lord of the Rings". The most powerful ring falls into the hands of a hobbit named Frodo Baggins, who is sent on a quest to destroy [[The One Ring]] deep within the enemy territory of [[Mordor]].

== Creation ==

The Lord of the Rings was published in three parts in the years 1954 and 1955, and was preceded by the prologue, ''[[The Hobbit]]''.

=== Writing ===
After the success of his earlier book ''[[The Hobbit]]'', Tolkien's publishers persuaded him to write a sequel. He began writing in December 1937, but the first drafts were still far away from the finished version. After writing and re-writing the beginning several times, Tolkien realized the role of the [[One Ring (Middle-earth)|One Ring]] and the quest it entailed in the spring of 1938, while writing the discussion between Gildor Inglorion and the later [[Frodo Baggins]]. This was the point upon which the back story and central quest that would be ''The Lord of the Rings'' came together in his mind. It was also the point that he firmly set the book's plot into his already existing [[Middle-earth]] legendarium. Whereas the ''The Hobbit'' had before been separate from his Middle-earth mythology, while still borrowing ideas, names, and persons from it, Tolkien now consciously moved it and its sequel into the Middle-earth setting. This resulted in the changes in tone, and in the meaning of formerly unimportant things as the 'magic ring' and the Necromancer, who both gained literary importance in the sequel. While the ''The Hobbit'' was written as a story intended for his children, ''The Lord of the Rings'' due to the realization of the later plot, soon became an epic tale of much greater proportions, both in plot and in length.

The earlier drafts and versions of ''The Lord of the Rings'' were published posthumously by his son Christopher Tolkien in ''The History of The Lord of the Rings'' (1988-1992), which are volumes VI–IX of ''The History of Middle-earth''.

In the story of the Middle-earth legendarium, ''The Hobbit'' appears as Bilbo's story of his journey and the finding of the Ring, while ''The Lord of the Rings'' are Frodo's later additions of the War of the Ring, both of which form the ''[[Red Book of Westmarch]]''.

=== Publication ===
Although often wrongly thought to be a [[trilogy]], ''The Lord of the Rings'' was conceived by the author as a single work. Its internal structure divides it into six 'books', named Book I-VI, according to the plot, with several appendices and an index. Because of paper shortages, the amount of paper needed and to reduce financial risk, it was released by the publisher [[Allen & Unwin]] in three volumes, each containing two Books:
#''[[The Fellowship of the Ring]]''
#''[[The Two Towers]]''
#''[[The Return of the King]]''
This resulted in the common error of calling ''The Lord of the Rings'' a [[trilogy]], a term which Tolkien rejected, just as he disliked the book being published in separate volumes. The first two volumes were published in 1954, and the third in 1955. It was initially published in hardbound.

In 1965 an American paperback publisher released a "pirated" paperback edition, paying Tolkien nothing, in the belief that Tolkien's copyright in the U. S. was defective because of a technicality. Tolkien reached a legal settlement with this publisher, and another publisher released an authorized edition for which Tolkien was paid royalties. The book was an instant success, particularly among college students.

== Story ==
=== Background story ===
In the [[Second Age (Middle-earth)|Second Age]] the Dark Lord [[Sauron]] created the [[One Ring (Middle-earth)|One Ring]] to help him conquer the peoples of Middle-earth. The [[Quendi|Elves]] and [[Man (Middle-earth)|Men]] of Middle-earth, led by High King Gil-galad of the [[Noldor]] and King Elendil of the [[Arnor|Dúnedain]], formed the ''[[Last Alliance of Elves and Men]]'' to fight him. Sauron was defeated and the Ring cut from his hand, thus the ''[[War of the Last Alliance]]'' ended, beginning the [[Third Age (Middle-earth)|Third Age]].

The story takes place at a time when the Elves, immortal and fairest of all beings in the world, are leaving the war-weary world to sail to the blessed realm of [[Valinor]]. With the departure of the Elves, the Age of Men has come. But the Dark Lord [[Sauron]], not truly killed at the end of the last Age, has been regaining power over the millennia since his defeat. Instrumental in his survival was the [[One Ring (Middle-earth)|One Ring]], which had kept him alive, and for which he now searches. This Ring, which had been lost for millennia, fell by chance into the hands of the [[hobbit]] [[Bilbo Baggins]], the story of which is told in ''[[The Hobbit]]''. At the beginning of ''The Lord of the Rings'', sixty years have passed since Bilbo found the One Ring.

=== The Fellowship of the Ring ===
==== Book I ====
The [[Hobbit]] [[Bilbo Baggins]] celebrates his 111th birthday, after which he leaves [[Shire (Middle-earth)|the Shire]] to travel once more, leaving his home Bag End and his [[One Ring (Middle-earth)|magic ring]] to his heir [[Frodo Baggins|Frodo]].

In [[Middle-earth chronology|T.A.]] 3018, Frodo is visited by his old friend, the Wizard [[Gandalf]], who tells him of the Ring's history and gives him the task of taking the Ring to the [[Quendi|Elven]] refuge [[Rivendell]]. Frodo leaves the Shire joined by his friends [[Samwise Gamgee|Sam Gamgee]], [[Meriadoc Brandybuck|Merry Brandybuck]], and [[Peregrin Took|Pippin Took]], all the while pursued by the mysterious otherworldly [[Nazgûl|Black Riders]], servants of Sauron. After an adventurous time they arrive in [[Breeland|Bree]], where they meet the human Ranger [[Aragorn|Strider]]. With his help they manage the make the last stretch of the way to the Ford of [[Bruinen]] at Rivendell.

==== Book II ====
The group have made it to [[Rivendell]], where the Council of Elrond decides over further action. The Ring shall be destroyed, which can only be done in [[Mount Doom]] in Sauron's land [[Mordor]] where it was forged. A group of companions are chosen to accompany Frodo on his quest, forming the Fellowship of the Ring: the hobbits Frodo, Sam, Merry, and Pippin, the Wizard [[Gandalf|Gandalf the Grey]], [[Gimli son of Glóin|Gimli]] the Dwarf, [[Legolas]] the Elf, and the Men [[Boromir]] of [[Gondor]] and [[Aragorn|Aragorn of the Dúnedain]]. The Fellowship journeys south, and after failing to cross the [[Misty Mountains]], goes under them through the Dwarven [[Khazad-dûm|Mines of Moria]]. There they are attacked by Orcs and lose their leader Gandalf to the [[Balrog]]. The Fellowship rest in the Elven realm [[Lothlórien]], and continue by boat down the river [[Anduin]]. At the Falls of Rauros they rest again, and Boromir tries unsuccessfully to take the Ring from Frodo. While the Fellowship searches for him, Frodo secretly leaves them behind to continue his quest all by himself, but Sam catches up with him and joins him on his way to Mordor.

=== The Two Towers ===
==== Book III ====
Boromir is mortally wounded defending Merry and Pippin from Orcs. Aragorn, Legolas, and Gimli decide to follow the Orcs into [[Rohan (Middle-earth)|Rohan]] to rescue the kidnapped hobbits. Merry and Pippin manage to escape [[Saruman]]'s Orcs at [[Fangorn|Fangorn Forest]], where they meet [[Treebeard]] the Ent. The tree-like Ents hold council, and decide to attack Saruman at [[Isengard]]. In Fangorn Forest Aragorn, Legolas, and Gimli meet the returned Gandalf the White, who takes them to the capital [[Edoras]], where they join [[Théoden|King Théoden of Rohan]] in the fight against Saruman. The forces of Rohan prevail against Saruman's armies in the ''Battle of the [[Helm's Deep|Hornburg]]''. Afterwards they go to Isengard to confront Saruman, whom is cast out of the Order by Gandalf. Pippin picks up the ''[[palantír]]'', and alerts Sauron to their presence. Gandalf and Pippin set of for [[Gondor]].

==== Book IV ====
Back in the Emyn Muil, Frodo and Sam journey east towards Mordor, trailed by [[Gollum]]. They capture him and he promises to lead them on their way. They travel though the Dead Marshes to the [[Morannon|Black Gate]], where Gollum leads them south. In [[Ithilien]] they are captured by [[Faramir]] of Gondor, but he releases them after hearing about their quest. Gollum leads them to and abandons them at the Pass of [[Cirith Ungol]], where they are attacked by the giant spider Shelob. Assuming Frodo dead, Sam takes the Ring to finish the quest on his own. Frodo's body is taken by a patrol of Orcs, who reveal that Frodo is only paralyzed. Sam, who has secretly followed them, tries to rescue Frodo, but is late and locked out of the Tower of Cirith Ungol.

=== The Return of the King ===
==== Book V ====
Gandalf and Pippin arrive in the city of [[Minas Tirith]], where they meet [[Denethor|Steward Denethor II]] of Gondor, and Pippin enters his service. Aragorn and his companions are joined by a group of Rangers from Rivendell. They go through the [[Ered Nimrais|Paths of the Dead]] and Aragorn summons the Dead Men of Dunharrow to his aid, and then rides east. King Théoden is summoned to Gondor, and the Rohirrim and Merry ride to Minas Tirith. Minas Tirith is besieged by the Sauron's armies. The following ''Battle of the [[Pelennor Fields]]'' is won with the help of the Rohirrim and the arrival of Aragorn with reinforcements from the southern regions of Gondor. Théoden is killed, but Éowyn and Merry slay the [[Witch-king of Angmar]]. Aragorn leads the combined forces of the West against Sauron in a move to distract him from Frodo, resulting in the ''Battle of the [[Morannon|Black Gate]]''.

==== Book VI ====
Sam rescues Frodo and returns the Ring to him. They continue the trek across Mordor. At Mount Doom they are attacked by Gollum. Frodo succumbs to the power of the Ring, claims it as his own and puts it on. Gollum fights him, biting off his finger and taking the Ring, but slips and falls into the [[Sammath Naur|Cracks of Doom]], destroying the Ring. Sauron is defeated and his power crumbles. The ''Battle of the Black Gate'' is won, and Gandalf sends the Eagles to rescue Frodo and Sam. Aragorn becomes King of Arnor and Gondor. Everyone returns homeward, and the hobbits return to [[Shire (Middle-earth)|the Shire]]. The land has been taken over by Saruman and his men, but after the ''Scouring of the Shire'' led by the returned hobbits, Saruman is killed and the hobbits can begin reordering their land. After a few years Frodo, who has been greatly hurt and burdenend though his quest and the Ring, traveled to the [[Mithlond|Grey Havens]]. There he bids his hobbit-friends good-bye, and leaves together with Bilbo, Gandalf, Elrond and Galadriel for the Undying Lands in the West, ending the [[Third Age (Middle-earth)|Third Age]] of Middle-earth. Sam, Merry and Pippin return to the Shire and their homes.

=== Appendices ===
''The Lord of the Rings'' is followed by six appendices, which give more background and detail on the history, peoples, languages, and various other topics of Middle-earth.
* '''Appendix A Annals of the Kings and Rulers''': contains further information on the history of [[Númenor]], [[Arnor]] and [[Gondor]], and of the [[Lôgrad|Rohirrim]] and [[Durin's Folk]].
* '''Appendix B The Tale of Years (Chronology of the Westlands)''': contains the timeline and chronicles of the [[Middle-earth chronology|Ages]].
* '''Appendix D Calendars''': the different [[Middle-earth chronology|calendar systems]].
* '''Appendix E Writing and Spelling''': on the pronunciation and the [[Tolkien's scripts|scripts]].
* '''Appendix F''': overview of the [[Tolkien's languages|languages]], and notes on the fictional "translation" of the book from the [[Westron]] language.

== Reception ==
From the beginning, ''The Lord of the Rings'' has received very mixed reviews, which range from high praise to condemnation. ''The Lord of the Rings'' has been considered one of the most influential works on the modern time [[fantasy]] genre.

In 1965, a US-American pirated paperback edition and the surrounding trouble spread awareness of ''The Lord of the Rings'' in the United States, where it soon gained a strong following.

Many times people have tried to interpret ''The Lord of the Rings'' as an [[allegory]]. Tolkien himself renounced that claim, stating he disliked allegory and that the ''The Lord of the Rings'' was not an allegory, which he also explained in the foreword to the book's second edition. Instead of being allegorical, he said that the book had a quality he called "applicability": because it was a story about universal themes and struggles, it could be likened to almost any situation in real life.<ref>"As for any inner meaning or 'message', it has in the intention of the author none. It is neither allegorical nor topical. [...] The real war does not resemble the legendary war in its process or its conclusion. [...] Other arrangements could be devised according to the tastes or views of those who like allegory or topical reference. But I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history, true or feigned, with its varied applicability to the thought and experience of readers. I think that many confuse 'applicability' with 'allegory'; but the one resides in the freedom of the reader, and the other in the purposed domination of the author.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref> This universality would result in it often being interpreted as an allegory, sometimes ironically from opposing ideological sides. For instance, J. R. R. Tolkien was a [[Roman Catholic]], and despite his statements that ''The Lord of the Rings'' was not an allegory some readers have seen [[Christian]] undertones in ''The Lord of the Rings.'' <ref>"Much as it is possible to identify allegories of the Second World war into ''The Lord of the Rings'', it is possible to identify any number of Christian allegories as well" in Smith, J. and Matthews, J.C. ''The Lord of the Rings: the Films, the books, the radio series'' (Virgin Books 2004), p.116.</ref> Tolkien himself specifically discounted the belief that he wrote the book as a direct Christian allegory—or any other sort of allegory, which he went on record as "cordially disliking" and saw as besides the point of good storytelling in the medieval sense, and preferring "applicability"—in contrast with the overt and acknowledged allegories in the works of Tolkien's friend, [[C. S. Lewis]].<ref>''The Letters of J. R. R. Tolkien'', #129</ref>

Tolkien's scarring experiences in [[World War I]] and his distaste for destructive industrialism - seen in the books in his characterization of [[Saruman]]'s armies - has been an influence on his works, as acknowledged by himself.<ref>"An author cannot, of course, remain wholly unaffected by his experience [...] One has indeed personally to come under the shadow of war to feel fully its oppression; but as the years go by it seems now often forgotten that to be caught in youth by 1914 was no less hideous an experience than to be involved in 1939 and the following years. [...] It has indeed some basis in experience, though slender (for the economic situation was entirely different), and much further back. The country in which I lived in childhood was being shabbily destroyed before I was ten, in days when motor-cars were rare objects (I had never seen one) and men were still building suburban railways. Recently I saw in a paper a picture of the last decrepitude of the once thriving corn-mill beside its pool that long ago seemed to me so important.", J. R. R. Tolkien, ''The Lord of the Rings'', Foreword</ref><ref>John Garth, "Tolkien and the Great War: The Threshold of Middle Earth," available at [https://www.amazon.com/Tolkien-Great-War-Threshold-Middle-earth/dp/0618331298 Amazon.com].</ref> However, Tolkien did state that "The Lord of the Rings is, of course, a fundamentally religious and Catholic work; unconsciously so at first, but consciously in the revision[]"—which indicates his devoted faith.<ref>[https://www.grin.com/document/22410]</ref>

Many have criticised Tolkien's adaptation of Eowyn in the third book: ''The Return of The King''. The fact that she is feautered in combat is generally considered to be an anti-conservative. The fact that the military should be reserved for men has also been endorsed by vice-president Mike Pence. Due to this, Swedish translator Åke Ohlmark later edited the chapter: ''The Battle of Pelennor Fields'' so that Merry Brandybuck was the one who killed the which-king, rather than Eowyn. Åhlmark said that the edit was closer to Tolkiens original vision and claimed that Tolkien might have intended it to be Merry who milled the which king all along. The original text: 'Then tottering, struggling up, with her last strength she drove her sword between crown and mantle, as the great shoulders bowed before her.' is believed to be a typo where Tolkien intended to have ''him'' instead of ''her''. This was corrected by Åhlmark in the Swedish translation of the book.

== Sequel ==

Tolkien attempted to write a sequel to ''The Lord of the Rings''. Although he did a first draft, he would never complete it. The unfinished work is now part of the 12th volume of ''The History of Middle-earth'', under the title of ''The New Shadow''.

== Adaptions ==
''The Lord of the Rings'' has been adapted full or in part in a variety of media. Among these are films, stage plays and a musical.

=== The Lord of the Rings film trilogy ===
'''''The Lord of the Rings'' film trilogy''' were three films based on the book, all directed by [[Peter Jackson]], produced by [[New Line Cinema]] and filmed in [[New Zealand]]. The film titles were derived from the three volumes:

* ''[[The Fellowship of the Ring (film, 2001)|The Lord of the Rings: The Fellowship of the Ring]]'' (2001)
* ''[[The Two Towers (film, 2002)|The Lord of the Rings: The Two Towers]]'' (2002)
* ''[[The Return of the King (film, 2003)|The Lord of the Rings: The Return of the King]]'' (2003)

The films were released annually in cinemas from December 2001 to 2003. DVD releases of the cinema version and Special Extended Editions have also been released for each film. Each extended edition includes four discs, two of bonus material.

The Lord of the Rings film trilogy received universal acclaim from critics and fans alike. Some even cited it as "the [[Star Wars]] Trilogy for [[Millennials]]". The trilogy had 30 [[Academy Awards|Oscar]] nominations, 17 of which it won. One of them being Best Picture, which was won by ''The Return of the King'' at the 76th Academy Awards in 2004. ''The Return of the King'' is also the only film in cinematic history that won every Oscar it was nominated for, 11 in all. It is tied with ''[[Titanic (1997 film)|Titanic]]'' and ''[[Ben-Hur (1959 film)|Ben-Hur]]'' as the film that won the most Academy Awards in cinematic history.<ref>[http://www.filmsite.org/oscars2.html#1]</ref> Both the first and third films in the series also won [[Movieguide]]'s "Best Movie for Mature Audiences" award in 2002 and 2004, respectively.<ref>[https://movieguideawards.com/category/winners/]</ref>

== References ==
{{reflist|2}}

== See also ==
*''[[The Hobbit]]''

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