Squaring the Circle/Historical Note

Historical Note on Squaring the Circle

The problem of squaring the circle using a compass and straightedge construction dates from the time of Anaxagoras of Clazomenae, who considered the question while in prison for political reasons.

It subsequently became an exercise that the ancient Greeks tried but 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): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): squaring the circle
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): squaring the circle
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): squaring the circle
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