Theodor Reye
Encyclopedia
Theodor Reye was a German
mathematician
. He contributed to geometry, particularly projective geometry
and synthetic geometry
. He is best known for his introduction of configurations
in second edition of his book, Geometrie der Lage (Geometry of Position, 1876). The Reye configuration 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
: Construct all possible spheres that are simultaneously tangent to four given spheres.
s, quadric
s and projective geometry
.
Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced later work by Corrado Segre
on manifolds.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He contributed to geometry, particularly projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
and synthetic geometry
Synthetic geometry
Synthetic or axiomatic geometry is the branch of geometry which makes use of axioms, theorems and logical arguments to draw conclusions, as opposed to analytic and algebraic geometries which use analysis and algebra to perform geometric computations and solve problems.-Logical synthesis:The process...
. He is best known for his introduction of configurations
Configuration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.Although certain specific...
in second edition of his book, Geometrie der Lage (Geometry of Position, 1876). The Reye configuration 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
Problem of Apollonius
In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane . Apollonius of Perga posed and solved this famous problem in his work ; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived...
: Construct all possible spheres that are simultaneously tangent to four given spheres.
Life
Reye obtained his Ph.D. from the University of Göttingen 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 sectionConic section
In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...
s, quadric
Quadric
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in -dimensional space defined as the locus of zeros of a quadratic polynomial...
s and projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
.
Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced later work by Corrado Segre
Corrado Segre
Corrado Segre was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry....
on manifolds.