Julius Petersen
Julius Petersen ( born June 16, 1839 in Soro; † August 5, 1910 in Copenhagen) was a Danish mathematician. He was a pioneer in graph theory.
Life
Petersen was the son of a dyer's family was poor. He was a friend since childhood with Hieronymus Georg Zeuthen, who then lived a few houses from him. Even as a student he was interested in mathematics and tried his hand at the trisection of an angle with compass and straightedge, a classic ( and unsolvable ) geometric problem. In 1854 he had to leave school because his family could not support him, and went to an uncle in Kolding as an apprentice in a grocery store. After his uncle's death in 1855 he inherited some money and was able to finish school in Soro and study from 1856 at the Polytechnic Institute in Copenhagen. In 1860 he graduated as a civil engineer, but he had already in 1858 published a mathematical paper. Also in 1860 he sent an essay on the cycloid in a competition at the University of Copenhagen and won - but since he was not a student him the prize was not awarded. From 1859 he taught mathematics in a private school. In 1862 he passed the entrance examination to the University and began to study mathematics, while he taught at the same time and in 1862 married. The marriage produced two sons and a daughter were born. In 1866 he received his university degree in mathematics, won the 1867 Gold Medal of the University for a thesis on the equilibrium of floating bodies and in 1871 received his doctorate with a thesis on the possibility of construction by ruler and compass. 1870/71 he corresponded on the subject with Sylow. In 1871 he became a lecturer at the Polytechnic and in 1877 professor of mathematics at the University of Copenhagen, where he stayed the rest of his career. His colleague there was his friend Zeuthen. He also taught at the Military School from 1881 to 1887.
In 1891 he published a work in which he is considered a pioneer in graph theory, and the set of Petersen contained ( a cubic graph without a bridge has a 1-factor ).
He wrote a series of textbooks for students. Petersen published in 1880 a treatise on geometric constructions with ruler and compass (see also Classical problems of ancient mathematics), which appeared again in 1990 as a French translation.
Petersen is one of the founding members in 1873 of the Danish Mathematical Society.
Petersen discovered in 1898 the first Snark ( Petersen graph ). These are special cubic graphs whose edges can not be colored with three colors so that no two edges have the same color at a node. The four-color problem can be traced back to the question of the existence of planar snarks after Peter Guthrie Tait. More Snarks were discovered in 1946 by Danilo Blanusa and then by Blanche Descartes and others.
He dealt with a wide variety of fields, in addition to geometry and graph theory, among other things, mathematical economics ( he was a member of a company that dealt with economics and belonged to the well-known Danish intellectuals Georg Brandes ) and cryptography ( written in a paper in 1875, in French), number theory, combinatorics ( Latin squares ), invariant theory (at that time a very active field of research, which he corresponded with James Joseph Sylvester and which was the reason for his interest in graph theory), mechanics and function theory. He was on the advisory board of the insurance company Hafnia and from 1887 in the State Commission for secondary schools.
Writings
- Kinematics, Copenhagen 1884
- Textbook of dynamics of solids, Copenhagen 1887
- Theory of algebraic equations, Copenhagen 1878
- Lectures on Complex Analysis, Copenhagen 1898
- Methods and theories to resolve geometrical construction tasks: applied to about 400 tasks, Copenhagen 1879