What is Euler characteristic?, Explain Euler characteristic, Define Euler characteristic

~~~ Euler characteristic ~~~

Title: What is Euler characteristic?, Explain Euler characteristic, Define Euler characteristic
Created on: 2018-08-19

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Description: In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by χ {\displaystyle \chi } . The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids. Leonhard Euler, for whom the concept is named, introduced it for polyhedra but failed to rigorously prove that it is an invariant. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra.

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