Theodor Reye
   HOME

TheInfoList



OR:

Karl Theodor Reye (born 20 June 1838 in Ritzebüttel,
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
and died 2 July 1919 in
Würzburg Würzburg (; Main-Franconian: ) is a city in the region of Franconia in the north of the German state of Bavaria. Würzburg is the administrative seat of the ''Regierungsbezirk'' Lower Franconia. It spans the banks of the Main River. Würzburg is ...
,
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
) was a
German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...
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, structure, space, models, and change. History On ...
. He contributed to geometry, particularly
projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...
and
synthetic geometry Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compa ...
. He is best known for his introduction of configurations in the second edition of his book, ''Geometrie der Lage'' (Geometry of Position, 1876). The
Reye configuration In geometry, the Reye configuration, introduced by , is a configuration of 12 points and 16 lines. Each point of the configuration belongs to four lines, and each line contains three points. Therefore, in the notation of configurations, the Reye ...
of 12 points, 12 planes, and 16 lines is named after him. Reye also developed a novel solution to the following three-dimensional extension of the
problem of Apollonius In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 190 BC) posed and solved this famous problem in his work (', "Tangencies ...
: Construct all possible spheres that are simultaneously tangent to four given spheres.


Life

Reye obtained his Ph.D. from the
University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
in 1861. His dissertation was entitled "Die mechanische Wärme-Theorie und das Spannungsgesetz der Gase" (The mechanical theory of heat and the potential law of gases).


Mathematical work

Reye worked on
conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a specia ...
s,
quadric In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is de ...
s and
projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...
. Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced later work by
Corrado Segre Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry. Early life Corrado's parents were Abramo Segre and Estella De Ben ...
on manifolds. He introduced Reye congruences, the earliest examples of
Enriques surface In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity ''q'' = 0 and the canonical line bundle ''K'' is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex ...
s.


References


Further reading

* (NB. Theodor Reye was a polytechnician in Zürich in 1860, but later became a professor in Straßburg. This paper established ' and laid the foundation to what is known as '' Reye–Archard–Khrushchov wear law'' today.


External links

* * * Theodor Reye (1892
Die Geometrie der Lage
from
archive.org The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
. * * {{DEFAULTSORT:Reye, Theodor 1838 births 1919 deaths Geometers 19th-century German mathematicians University of Göttingen alumni ETH Zurich faculty RWTH Aachen University faculty University of Strasbourg faculty Heads of universities in Germany 20th-century German mathematicians