Search results
Felix Christian Klein ( German: [klaɪn]; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory. His 1872 Erlangen program classified geometries by their basic symmetry groups and ...
- Mathematics
- Edward Kasner
Apr 21, 2024 · Felix Klein (born April 25, 1849, Düsseldorf, Prussia [Germany]—died June 22, 1925, Göttingen, Germany) was a German mathematician whose unified view of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm, profoundly influenced mathematical developments.
- The Editors of Encyclopaedia Britannica
Jun 22, 2011 · Biography. Felix Klein is best known for his work in non-euclidean geometry, for his work on the connections between geometry and group theory, and for results in function theory. He was born on 25/4/1849 and delighted in pointing out that each of the day ( 5^ {2} 52), month ( 2^ {2} 22), and year ( 43^ {2} 432) was the square of a prime.
- Introduction. Structuralism in the philosophy of mathematics holds that mathematics is the science of abstract structures. An alternative characterization of the position does not assume structures as the subject matter of mathematics, but rather holds that mathematical theories study only the structural properties of their objects.1 The focus on such properties is closely related to criteria of structural identity of mathematical objects.
- Duality and Transfer Principles. The mathematical background of the Erlangen program is known to be rich and multifaceted.6 Klein’s group-theoretic approach in geometry has different roots, including algebraic work on permutations groups by Camille Jordan and Évariste Galois, Arthur Cayley’s invariant-theoretic approach in geometry, as well as Sophus Lie’s parallel work on geometry, to name just a few.
- Klein’s Erlangen Program. Klein’s program was first outlined in his “Vergleichende Betrachtungen über neuere geometrische Forschungen” (1872), a programmatic pamphlet distributed during his inauguration speech at the University of Erlangen.24 Klein presents here a novel method to study and to classify different geometries in terms of their corresponding transformation groups.
- Structuralist Themes. The geometrical research surveyed in the last two sections strongly contributed to a general structural turn in 19th-century mathematics.
People also ask
What is Klein geometry?
Who is Felix Klein?
What was Klein's major contribution to mathematics?
What was Klein's contribution to geometry in the 19th century?
Because of his edition of Julius Plücker’s work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23.
- Renate Tobies
In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts as the symmetry group of the geometry. For background and motivation see the article on the Erlangen program .
1.1 Felix Klein’s Upbringing, Education, and Academic Career. Felix Klein was born on April 25, 1849 in Düsseldorf, which was then the seat of government for the Rhine Province of the Prussian kingdom. He was the second of four children born to Peter Caspar Klein (1809–1889), a senior civil servant and chief treasurer of the Rhine Province ...
