Carl Hierholzer
Encyclopedia
Carl Hierholzer was a German
mathematician
.
from Ruprecht-Karls-Universität Heidelberg in 1865. His Ph.D.
advisor was Ludwig Otto Hesse (1811–1874). In 1870 Hierholzer wrote his habilitation
about conic sections (title: Ueber Kegelschnitte im Raum) in Karlsruhe, where he later became professor.
Hierholzer proved that a graph
has an Eulerian cycle if and only if it is connected and every vertex has an even degree. This result had been given, without proof, by Leonard Euler in 1736. Hierholzer apparently explained his proof, just before his premature death in 1871, to a colleague who then arranged for its posthumous publication which appeared in 1873 (title: Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren.)
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....
.
Biography
Hierholzer studied mathematics in Karlsruhe, and he got his Ph.D.Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Ruprecht-Karls-Universität Heidelberg in 1865. His Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
advisor was Ludwig Otto Hesse (1811–1874). In 1870 Hierholzer wrote his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
about conic sections (title: Ueber Kegelschnitte im Raum) in Karlsruhe, where he later became professor.
Hierholzer proved that a graph
Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
has an Eulerian cycle if and only if it is connected and every vertex has an even degree. This result had been given, without proof, by Leonard Euler in 1736. Hierholzer apparently explained his proof, just before his premature death in 1871, to a colleague who then arranged for its posthumous publication which appeared in 1873 (title: Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren.)