Euler calculus

For numerical analysis of ordinary differential equations, see Euler's method.

Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions^[1] by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem.^[2] It was introduced independently by Pierre Schapira^[3][4][5] and Oleg Viro^[6] in 1988, and is useful for enumeration problems in computational geometry and sensor networks.^[7]

See also

• Topological data analysis