Squaring the circle
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 Carl Louis Ferdinand von Lindemann in 1882.
The other two problems from antiquity are:
"Duplicating the cube"
- Construct the length of the side of a cube that would have half the volume of a cube of a given size, effectively constructing the number cube root of 2, and
"Trisecting an angle"
- Construct an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, and a compass.
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.
- Circle Squaring (mathworld.wolfram.com)
- Squaring the circle - Wikipedia
- What Does Squaring the Circle Mean? by Catherine Beyer (learnreligions.com)
- Who called pi transcendental (answers.com)
- (PDF) Pi is Transcendental: Von Lindemann's Proof Made Accessible to Today's Undergraduates, Randy K. Schwartz (academia.edu)
- Duplicating the cube, David Darling (daviddarling.info)
- Angle Trisection (mathworld.wolfram.com)
- Mathematical beauty: Beauty in method - Wikipedia a discussion of mathematical elegance