Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a
French
French may refer to:
* Something of, from, or related to France
** French language, which originated in France
** French people, a nation and ethnic group
** French cuisine, cooking traditions and practices
Arts and media
* The French (band), ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He entered the
École Normale Supérieure
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
in 1843 and received his doctoral degree in 1855 from the
Sorbonne. He was sought by
Urbain Le Verrier
Urbain Jean Joseph Le Verrier (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using only mathematics. ...
at the
Paris Observatory
The Paris Observatory (, ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centres in the world. Its historic building is on the Left Ban ...
, but chose instead to return to Thaon to study there. In 1859 he began to teach at
Bordeaux
Bordeaux ( ; ; Gascon language, Gascon ; ) is a city on the river Garonne in the Gironde Departments of France, department, southwestern France. A port city, it is the capital of the Nouvelle-Aquitaine region, as well as the Prefectures in F ...
.
In 1863 Hoüel expressed his doubts about the verifiability of the
parallel postulate
In geometry, the parallel postulate is the fifth postulate in Euclid's ''Elements'' and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a line segment intersects two straight lines forming two interior ...
of
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
.
In 1867 Hoüel produced French translations of two key publications of
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
:
Lobachevski
Nikolai Ivanovich Lobachevsky (; , ; – ) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, ...
's ''Geometrical Studies on the Theory of Parallels'' and
Bolyai's ''Science of Absolute Space''.
Hoüel published a four volume work titled ''Théorie Élémentaire des Quantités Complexes''. Volume four, published in 1874, began with a discussion of properties of algebraic operations (commutativity, associativity, distribution, and inverses) and used the algebra of
quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...
s and
versor
In mathematics, a versor is a quaternion of Quaternion#Norm, norm one, also known as a unit quaternion. Each versor has the form
:u = \exp(a\mathbf) = \cos a + \mathbf \sin a, \quad \mathbf^2 = -1, \quad a \in ,\pi
where the r2 = −1 conditi ...
s to describe
spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...
. However, in 1890
P. G. Tait revealed his dissatisfaction with Hoüel's changes in notation with text that Tait had given for Hoüel's use. Tait wrote:
:The earliest offender in this class was the late M. Hoüel who, while availing himself of my permission to reproduce, in his ''Théorie Élémentaire des Quantités Complexes'', large parts of this volume, made his pages absolutely repulsive by introducing fancied improvements in the notation.
In 1876 Hoüel reviewed a
Russian language
Russian is an East Slavic languages, East Slavic language belonging to the Balto-Slavic languages, Balto-Slavic branch of the Indo-European languages, Indo-European language family. It is one of the four extant East Slavic languages, and is ...
quaternion textbook written by Romer (1868)
[J. Hoüel (1876) "Principles fundamentaux de la Méthode de Quaternions", ''Bulletin ces Sciences Mathématiques et Astronomique'' 11: 113,4]
References
*
G. B. Halsted (1897
Guillaume-Jules Hoüel American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an exposi ...
4:99–101, link from
Jstor
JSTOR ( ; short for ''Journal Storage'') is a digital library of academic journals, books, and primary sources founded in 1994. Originally containing digitized back issues of academic journals, it now encompasses books and other primary source ...
early content.
*
*
{{DEFAULTSORT:Houel, Jules
People from Calvados (department)
1823 births
1886 deaths
Geometers
19th-century French mathematicians
Russian–French translators
19th-century French translators