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Line 1: − + + − ;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. It absolutely depends on your "point of view".+ + + + + Line 13:
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idiom category; other two problems from antiquity
'''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==
[[category:Mathematics]]
[[category:Mathematics]]
[[Category:Idioms]]