Hexagon set of Catalan

Hexagon set of Catalan

The Sechsecksatz of Catalan is a theorem of elementary geometry , which states the following:

In a hexagon of the Euclidean plane with corner points , the three diagonals of which are of the same length and whose opposite sides are parallel , which therefore fulfills and or or fulfills, the corner points always lie on a circle . ${\displaystyle A,B,C,D,E,F}$ ${\displaystyle {\overline {AD}}={\overline {BE}}={\overline {CF}}}$ ${\displaystyle {AB}\parallel {DE}}$ ${\displaystyle {BC}\parallel {EF}}$ ${\displaystyle {CD}\parallel {FA}}$ ${\displaystyle A,B,C,D,E,F}$

It is named after Eugène Charles Catalan .

literature

• Heinrich Dörrie : Mathematical miniatures . 2nd Edition. Sendet, Wiesbaden 1979, ISBN 3-500-21150-X (unchanged reprint of the 1943 edition).

References and comments

1. ^ Heinrich Dörrie : Mathematical miniatures . 2nd Edition. Sendet, Wiesbaden 1979, ISBN 3-500-21150-X , p. 38, 521 (unaltered reprint of the 1943 edition).
2. ↑ What is meant is a convex geometric figure .