Walther von Dyck
Encyclopedia
Walther Franz Anton von Dyck (6 December 1856 in Munich
– 5 November 1934 in Munich
), born Dyck and later ennobled
, was a German
mathematician
. He is credited with being the first to define a mathematical group
, in the modern sense in , and laid the foundations of combinatorial group theory
, being the first to systematically study a group by generators and relations.
The Dyck language
in formal language theory is named after him, as are Dyck's theorem and Dyck's surface in the theory of surface
s, together with the von Dyck groups, the Dyck tessellations, and the Dyck graph
.
Von Dyck was a student of Felix Klein
, and he was also the editor of Kepler's
works.
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
– 5 November 1934 in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
), born Dyck and later ennobled
Von
In German, von is a preposition which approximately means of or from.When it is used as a part of a German family name, it is usually a nobiliary particle, like the French, Spanish and Portuguese "de". At certain times and places, it has been illegal for anyone who was not a member of the nobility...
, was a German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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 is credited with being the first to define a mathematical group
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
, in the modern sense in , and laid the foundations of combinatorial group theory
Combinatorial group theory
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations...
, being the first to systematically study a group by generators and relations.
The Dyck language
Dyck language
In the theory of formal languages of computer science, mathematics, and linguistics, the Dyck language is the language consisting of balanced strings of parentheses [ and ]. It is important in the parsing of expressions that must have a correctly nested sequence of parentheses, such as arithmetic...
in formal language theory is named after him, as are Dyck's theorem and Dyck's surface in the theory of surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
s, together with the von Dyck groups, the Dyck tessellations, and the Dyck graph
Dyck graph
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck.It is Hamiltonian with 120 distinct Hamiltonian cycles. It has chromatic number 2, chromatic index 3, radius 5, diameter 5 and girth 6...
.
Von Dyck was a student of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
, and he was also the editor of Kepler's
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
works.