Finsler-Hadwiger theorem

The set of Finsler Hadwiger (by Paul Finsler and Hugo Hadwiger ) is a statement of the elementary geometry, a property of two squares with a common vertex describes.

For two squares and with a common point and midpoints and let and be the midpoints of the lines and , then the quadrangle is also a square. ${\ displaystyle \ square ABCD}$ ${\ displaystyle \ square AB ^ {\ prime} C ^ {\ prime} D ^ {\ prime}}$ ${\ displaystyle A}$ ${\ displaystyle F}$ ${\ displaystyle H}$ ${\ displaystyle E}$ ${\ displaystyle G}$ ${\ displaystyle B ^ {\ prime} D}$ ${\ displaystyle D ^ {\ prime} B}$ ${\ displaystyle \ square EFGH}$

Finsler and Hadwiger described this theorem in 1937 in an article on relations at the triangle, which also included the Hadwiger-Finsler inequality , which was later named after them .

literature

Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics . MAA 2010, ISBN 978-0-88385-348-1 , p. 125 ( books.google.de ).
Paul Finsler, Hugo Hadwiger: Some Relations in the Triangle . In: Commentarii Mathematici Helvetici , edition 10, 1937, pp. 316–326, especially p. 324

Web links

Commons : Finsler-Hadwiger set - collection of images, videos and audio files

Eric W. Weisstein : Finsler-Hadwiger theorem . In: MathWorld (English).