Editing Julius Petersen (section)

==Work==
Many of Petersen's early contributions to mathematics were mainly focused on geometry. During the 1860s he wrote five textbooks along with some papers, all on geometry. One of his most remarkable works was a book, ''‘Methods and Theories’''. The first edition of this book appeared only in Danish, but the 1879 edition was translated into eight different languages including English, French, and Spanish, earning him an international reputation more than any of his other works.

In graph theory, two of Petersen's most famous contributions are: the Petersen graph, exhibited in 1898, served as a counterexample to Tait's ‘theorem’ on the 4-colour problem: a bridgeless 3-regular graph is factorable into three 1-factors and the theorem: ''‘a connected 3-regular graph with at most two leaves contains a 1-factor’''.

In 1891 Petersen published a paper in the Acta Mathematica (volume 15, pages 193–220) entitled ''‘Die Theorie der regularen graphs’''. It was the first paper containing (correct) results explicitly in graph theory. The paper consisted of four major parts:
:(i) The transformation of the original algebraic problem into a graph theoretical one
:(ii) The problem of factorizing regular graphs of even degree. Here Petersen proves his first major result, viz. that any such graph has a 2-factorization ([[2-factor theorem]]).
:(iii) Criteria for the existence of edge-separating factorizations of 4-regular graphs.
:(iv) The factorization of regular graphs of odd degree, in particular, the theorem that any bridgeless 3-regular graph can be decomposed into a l-factor and a 2-factor ([[Petersen's theorem]]).

Between 1887 and 1895 Petersen also contributed to mathematics with different models and instruments. one of these models was a ‘eine Serie von kinematischen Modellen’ which in 1888 was asked by ‘Verlagsbuchhandler L. Brill’ for permission to produce and sell. In 1887 Petersen had constructed another model; a [[planimeter]] which was presented to the [[Royal Danish Academy of Science and Letters]]. It consisted of an arm, of, whose one end o is fixed to the paper by a lead cylinder with a pin p, and whose other end f is connected to a second arm dc (or df) of length L. When the stylus d is moved around the domain once, the area is measured as L∫dh, where dh is the differential displacement of the arm dc orthogonal to itself.<ref>{{cite book|url=https://books.google.com/books?id=zESPDAAAQBAJ&pg=PA48|title=The Julius Petersen Graph Theory Centennial|first1=L. D.|last1=Andersen|first2=J.|last2=Bang-Jensen|first3=T. R.|last3=Jensen|first4=L. K.|last4=Jørgensen|first5=G.|last5=Sabidussi|first6=C.|last6=Thomassen|first7=B.|last7=Toft|first8=P. D.|last8=Vestergaard|date=6 June 2016|publisher=Elsevier|via=Google Books|isbn=9781483296326}}</ref>