Pierre Wantzel

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Pierre Laurent Wantzel
Born (1814-06-05)June 5, 1814
Paris, France
Died May 21, 1848(1848-05-21) (aged 33)
Paris, France
Residence France
Fields Mathematics
Known for Solving several ancient Greek geometry problems

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, and
  2. trisecting the angle

are impossible to solve if one uses only compass and straightedge. In the same paper he also solved the problem of determining which regular polygons are constructible:

  1. a regular polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes (i.e. that the sufficient conditions given by Carl Friedrich Gauss are also necessary)

The solution to these problems had been sought for thousands of years, particularly by the ancient Greeks.

"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]

References[edit]

  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. 

External links[edit]