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In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century. [12] [11] His 866 publications and his correspondence are being collected in the Opera Omnia Leonhard Euler which, when completed, will consist of 81 quartos.
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [2]
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy [21] and L'Huilier, [22] and represents the beginning of the branch of mathematics known as topology. More than one century after Euler's paper on the bridges of Königsberg and while Listing was introducing the concept ...
Usually, Euler's equation refers to one of (or a set of) differential equations (DEs). It is customary to classify them into ODEs and PDEs. Otherwise, Euler's equation may refer to a non-differential equation, as in these three cases: Euler–Lotka equation, a characteristic equation employed in mathematical demography; Euler's pump and turbine ...
Euler's theorem and its proof are contained in paragraphs 24–26 of the appendix (Additamentum. pp. 201–203) of L. Eulero (Leonhard Euler), Formulae generales pro translatione quacunque corporum rigidorum (General formulas for the translation of arbitrary rigid bodies), presented to the St. Petersburg Academy on October 9, 1775, and first ...
Leonhard Euler is credited of introducing both specifications in two publications written in 1755 [3] and 1759. [4] [5] Joseph-Louis Lagrange studied the equations of motion in connection to the principle of least action in 1760, later in a treaty of fluid mechanics in 1781, [6] and thirdly in his book Mécanique analytique. [5]