Finsler–Hadwiger theorem

Finsler-Hadwiger theorem

The Finsler–Hadwiger theorem is statement in Euclidean plane geometry that describes a third square derived from any two squares that share a vertex. The theorem is named after Paul Finsler and Hugo Hadwiger, who published it in 1937 as part of the same paper in which they published the Hadwiger–Finsler inequality relating the side lengths and area of a triangle.[1]

To state the theorem, suppose that ABCD and AB'C'D' are two squares with common vertex A. Let E and G be the midpoints of B'D and D'B respectively, and let F and H be the centers of the two squares. Then the theorem states that the quadrilateral EFGH is s square as well.[2]

References

  1. ↑ Finsler, P.; Hadwiger, H. (1937), "Einige Relationen im Dreieck", Commentarii Mathematici Helvetici (in German), 10 (1): 316–326, doi:10.1007/BF01214300, MR 1509584. See in particular p. 324.
  2. ↑ Alsina, Claudi; Nelsen, Roger B. (2010), "The Finsler–Hadwiger Theorem 8.5", Charming Proofs: A Journey Into Elegant Mathematics, Mathematical Association of America, p. 125, ISBN 9780883853481.
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