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.
In a paper from 1837[1], Wantzel proved that the problems of
- doubling the cube
- trisecting the angle and
- constructing a regular polygon whose number of sides is not the product of a power of 2 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.
References
- ^ M. [sic] 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. http://visualiseur.bnf.fr/ConsulterElementNum?O=NUMM-16381&Deb=374&Fin=380&E=PDF.
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