Hadwiger

Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.

Although born in Karlsruhe, Germany, Hadwiger grew up in Bern, Switzerland. He did his undergraduate studies at the University of Bern, where he majored in mathematics but also studied physics and actuarial science. He continued at Bern for his graduate studies, and received his Ph.D. in 1936 under the supervision of Willy Scherrer. He was for more than forty years a professor of mathematics at Bern.

Hadwiger's theorem in integral geometry classifies the possible isotropic measures on compact convex sets in d-dimensional Euclidean space. According to this theorem, any such measure can be expressed as a linear combination of d + 1 fundamental measures; for instance, in two dimensions, there are three possible measures of this type, one corresponding to area, a second corresponding to perimeter, and a third corresponding to the Euler characteristic.

The Hadwiger–Finsler inequality, proven by Hadwiger with Paul Finsler, is an inequality relating the side lengths and area of any triangle in the Euclidean plane. It generalizes Weitzenböck's inequality and was generalized in turn by Pedoe's inequality. In the same 1937 paper in which Hadwiger and Finsler published this inequality, they also published the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex.

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