Squaring the Circle/Historical Note
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Historical Note on Squaring the Circle
The construction of a square with the same area as a given circle, using a compass and straightedge construction, was an exercise that the ancient Greeks failed to succeed in.
This was one of three such problems: the other two being Trisecting the Angle and Doubling the Cube.
There are several techniques available that use other tools, but these were considered unacceptably vulgar to the followers of Plato.
The problem remained unsolved until its impossibility was proved in $1882$ by Ferdinand von Lindemann.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.18$: Algebraic and Transcendental Numbers. $e$ is Transcendental
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): squaring the circle