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addn info - full name Carl Louis Ferdinand von Lindemann - two external links http://answers.com/Q/Who_called_pi_transcendental and https://www.academia.edu/10775717/Pi_is_Transcendental_Von_Lindemann_s_Proof_Made_Accessible_to_Today_s_Undergraduates
'''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.
: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.
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 Carl Louis Ferdinand von 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.
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.
[https://www.learnreligions.com/squaring-the-circle-96039 What Does Squaring the Circle Mean? by Catherine Beyer (learnreligions.com)]
[https://www.learnreligions.com/squaring-the-circle-96039 What Does Squaring the Circle Mean? by Catherine Beyer (learnreligions.com)]
[http://answers.com/Q/Who_called_pi_transcendental Who called pi transcendental (answers.com)]
[https://www.academia.edu/10775717/Pi_is_Transcendental_Von_Lindemann_s_Proof_Made_Accessible_to_Today_s_Undergraduates (PDF) Pi is Transcendental: Von Lindemann's Proof Made Accessible to Today's Undergraduates, Randy K. Schwartz (academia.edu)]
[[category:Mathematics]]
[[category:Mathematics]]
[[Category:Idioms]]
[[Category:Idioms]]