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The solution to these problems had been sought for thousands of years, particularly by the ancient Greeks. However, Wantzel's work was neglected by his contemporaries and essentially forgotten. Indeed, it was only 50 years after its publication that
Wantzel's article was mentioned either in a journal
208:
Ordinarily he worked evenings, not lying down until late; then he read, and took only a few hours of troubled 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,
196:), then the roots cannot be expressed from the coefficients using real radicals alone; that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals. This theorem would be rediscovered decades later by (and sometimes attributed to)
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Wantzel is often overlooked for his contributions to mathematics. In fact, for over a century there was great confusion as to who proved the impossibility theorems.
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Wantzel was also the first person to prove, in 1843, that if a cubic polynomial with rational coefficients has three real roots but is irreducible in
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Disertaciones matemáticas sobre la cuadratura del cĂrculo: El metodo de
Wantzel y la divisiĂłn de la circunferencia en partes iguales
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more than 80 years after the publication of
Wantzel's article that his name started to be well known among mathematicians.
427:
367:
LĂĽtzen, Jesper (2009), "Why was
Wantzel overlooked for a century? The changing importance of an impossibility result",
289:[Investigations into means of knowing if a problem of geometry can be solved with a straightedge and compass],
287:"Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas"
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which he taunted at pleasure by all sorts of abuse. He brought sadness to those who mourn his premature death.
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311:(1887), "Metodo de Wantzel para conocer si un problema puede resolverse con la recta y el circulo",
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428:"ScienceDirect.com | Science, health and medical journals, full text articles and books"
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Profile from School of
Mathematics and Statistics; University of St Andrews, Scotland
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article or in a textbook. Before that, it seems to have been mentioned only once, by
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342:(in Spanish), Imprenta de la Viuda Ă© Hijo de D. E. Aguado, archived from
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Revista de los
Progresos de las Ciencias Exactas, FĂsicas y Naturales
144:. In the same paper he also solved the problem of determining which
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401:"Classification des nombres incommensurables d'origine algébrique"
109:(5 June 1814 in Paris – 21 May 1848 in Paris) was a French
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In a paper from 1837, Wantzel proved that the problems of
458:, Princeton University Press, pp. 34–37, 2019-10-08
485:
243:
75:Solving several ancient Greek geometry problems
164:(i.e. that the sufficient conditions given by
117:problems were impossible to solve using only
291:Journal de Mathématiques Pures et Appliquées
156:the number of its sides is the product of a
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215:Adhémar Jean Claude Barré de Saint-Venant
140:are impossible to solve if one uses only
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217:, on the occasion of Wantzel's death.
152:a regular polygon is constructible
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504:19th-century French mathematicians
409:Nouvelles Annales de Mathématiques
146:regular polygons are constructible
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113:who proved that several ancient
16:French mathematician (1814–1848)
263:10.1090/s0002-9904-1918-03088-7
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383:10.1016/j.hm.2009.03.001
246:"Pierre Laurent Wantzel"
244:Cajori, Florian (1918).
142:compass and straightedge
119:compass and straightedge
456:Tales of Impossibility
220:
107:Pierre Laurent Wantzel
23:Pierre Laurent Wantzel
432:www.sciencedirect.com
250:Bull. Amer. Math. Soc
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370:Historia Mathematica
285:Wantzel, L. (1837),
166:Carl Friedrich Gauss
135:trisecting the angle
193:casus irreducibilis
168:are also necessary)
129:doubling the cube
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81:Scientific career
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349:on 4 June 2016
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53:(1848-05-21)
499:1848 deaths
494:1814 births
399:L. (1843),
202:Otto Hölder
91:Mathematics
64:Nationality
51:21 May 1848
39:5 June 1814
488:Categories
462:2023-09-10
452:"TANGENT:"
437:2023-09-10
226:References
35:1814-06-05
416:: 117–127
395:Wantzel,
297:: 366–372
115:geometric
333:(1887),
212:—
95:Geometry
272:1560082
353:15 May
319:: 1–47
270:
87:Fields
67:French
404:(PDF)
347:(PDF)
340:(PDF)
131:, and
355:2016
200:and
48:Died
29:Born
379:doi
258:doi
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