Difference between revisions of "Circle"

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[[Image:265px-Circle Area svg.png|right|thumb|Area of the circle = '''''π''''' × area of the shaded square]]
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[[Image:265px-Circle Area svg.png|right|thumb|Area of the circle = <math>\pi</math> × area of the shaded square]]
A circle is the [[set]] of all the points in a given [[plane]] that are the same distance from a given [[point]] called the center.
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A '''circle''' is the [[set]] of all the points in a given [[plane]] that are the same distance, called the [[radius]], ''r'', from a given [[point]] called the center.
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A circle may also be defined [[algebra]]ically, as the solutions to an equation of the form:
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:<math>x^2 + y^2 = r^2</math>
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The measure of the line that forms the circle, or circumference, is given by:
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:<math>C = 2\pi*r</math>
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The area inside the circle is calculated using the formula:
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:<math>A = \pi*r^2</math>
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A circle is a [[conic section]], the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.
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Circles can readily be constructed by using a fixed distance between a pencil point and the center.  A [[compass]] is a tool for doing this easily.
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A circle with <math>r = 1</math> is called the ''unit circle'', and is used extensively in [[trignometry]].
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]
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[[category:mathematics]]

Revision as of 13:05, 22 April 2007

Area of the circle = × area of the shaded square

A circle is the set of all the points in a given plane that are the same distance, called the radius, r, from a given point called the center.

A circle may also be defined algebraically, as the solutions to an equation of the form:

The measure of the line that forms the circle, or circumference, is given by:

The area inside the circle is calculated using the formula:

A circle is a conic section, the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.

Circles can readily be constructed by using a fixed distance between a pencil point and the center. A compass is a tool for doing this easily.

A circle with is called the unit circle, and is used extensively in trignometry.