Difference between revisions of "Squaring the circle"
(→External links: added https://en.wikipedia.org/wiki/Squaring_the_circle Squaring the circle - Wikipedia] [https://www.learnreligions.com/squaring-the-circle-96039 What Does Squaring the Circle Mean? by Catherine Beyer) |
(idiom category; other two problems from antiquity) |
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'''Squaring the Circle''' refers to a classic mathematical challenge originated in [[Classical Antiquity|classical antiquity]]: | '''Squaring the Circle''' refers to a classic mathematical challenge originated in [[Classical Antiquity|classical antiquity]]: | ||
| − | :Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted by Anaxagoras. It was finally proved to be an impossible problem when pi was proven to be transcendental by Lindemann in 1882. | + | :Construct a square equal in area to a circle using only a straightedge and compass. |
| + | This was one of the three geometric problems of antiquity, and was perhaps first attempted by Anaxagoras. It was finally proved to be an impossible problem when pi was proven to be transcendental by Lindemann in 1882. | ||
| − | + | The other two problems from antiquity are "duplicating the cube" (constructing the length of the side of a cube that would have half the volume of a cube of a given side, effectively constructing the number cube root of 2) and "trisecting an angle". These three problems were finally shown to be unsolvable by straightedge and compass with the algebraic tools of the 19<sup>th</sup> century. | |
| − | + | ||
| + | Squaring the circle is sometimes used as an idiom in common discourse to mean taking on an impossible task. | ||
| + | |||
| + | ==Joke about the section of a cylinder as a squared circle== | ||
| + | As a joke, a circle can simultaneously present a square if a perfectly round [[cylinder]] is produced with a sectional length equal to its measured diameter. Looked at from the side it presents a square configuration. Looked at from the end it presents a circular configuration. The circle coexists as a square object and the square coexists as a circular object. The circle has been squared and the square has been circled, by the shaping of one cylinder. No one takes this seriously as being related to the classical problem. | ||
==External links== | ==External links== | ||
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[[category:Mathematics]] | [[category:Mathematics]] | ||
| + | [[Category:Idioms]] | ||
Revision as of 01:11, June 17, 2019
Squaring the Circle refers to a classic mathematical challenge originated in classical antiquity:
- Construct a square equal in area to a circle using only a straightedge and compass.
This was one of the three geometric problems of antiquity, and was perhaps first attempted by Anaxagoras. It was finally proved to be an impossible problem when pi was proven to be transcendental by Lindemann in 1882.
The other two problems from antiquity are "duplicating the cube" (constructing the length of the side of a cube that would have half the volume of a cube of a given side, effectively constructing the number cube root of 2) and "trisecting an angle". These three problems were finally shown to be unsolvable by straightedge and compass with the algebraic tools of the 19th century.
Squaring the circle is sometimes used as an idiom in common discourse to mean taking on an impossible task.
Joke about the section of a cylinder as a squared circle
As a joke, a circle can simultaneously present a square if a perfectly round cylinder is produced with a sectional length equal to its measured diameter. Looked at from the side it presents a square configuration. Looked at from the end it presents a circular configuration. The circle coexists as a square object and the square coexists as a circular object. The circle has been squared and the square has been circled, by the shaping of one cylinder. No one takes this seriously as being related to the classical problem.
External links
Circle Squaring (mathworld.wolfram.com)
Squaring the circle - Wikipedia
What Does Squaring the Circle Mean? by Catherine Beyer (learnreligions.com)