Pierre Wantzel

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Pierre Laurent Wantzel (June 5, 1814 in Paris – May 21, 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.[1]

In a paper from 1837,[2] Wantzel proved that the problems of

  1. doubling the cube
  2. trisecting the angle and
  3. constructing a regular polygon whose number of sides is not the product of a power of two and any number of distinct Fermat primes (i.e. that does not fulfill the same conditions proven to be sufficient by Carl Friedrich Gauss)

the solution to which had been sought for thousands of years, particularly by the ancient Greeks, were all impossible to solve if one uses only compass and straightedge.

"Ordinarily he worked evenings, not lying down until late; then he read, and took only a few hours of trouble sleep, making alternately wrong use of coffee and opium, and taking his meals at irregular hours until he was married. He put unlimited trust in his constitution, very strong by nature, which he taunted at pleasure by all sorts of abuse. He brought sadness to those who mourn his premature death." -- Adhémar Jean Claude Barré de Saint-Venant on the occasion of Wantzel's death.[3]


  1. ^ Cajori, Florian (1918). "Pierre Laurent Wantzel". Bull. Amer. Math. Soc. 24 (7): 339–347. doi:10.1090/s0002-9904-1918-03088-7. MR 1560082. 
  2. ^ M. L. Wantzel (1837). "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas". Journal de Mathématiques Pures et Appliquées 1 (2): 366–372. 
  3. ^ Florian Cajori (1922). "A History of Mathematics". p. 350. 

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