Maxwell's theorem

Routes with the same markings are parallel.
If the sides of the triangle are parallel to the cevans of the triangle that intersect at one point , then cevans of the triangle that are parallel to the corresponding sides of the triangle also intersect at a common point ${\displaystyle A'B'C'}$ ${\displaystyle V}$ ${\displaystyle ABC}$ ${\displaystyle A'B'C'}$ ${\displaystyle ABC}$ ${\displaystyle V'}$

The following statement about triangles in the plane is called Maxwell's theorem :

For a given triangle and a point that does not lie on the sides of the triangle, construct another triangle so that the side is parallel to the line , the side is parallel to the line and the side is parallel to the line . Then cut to the parallel to through , the parallel to through and parallel to through in a common point . ${\displaystyle ABC}$ ${\displaystyle V}$ ${\displaystyle A'B'C'}$ ${\displaystyle A'B'}$ ${\displaystyle CV}$ ${\displaystyle A'C'}$ ${\displaystyle BV}$ ${\displaystyle B'C'}$ ${\displaystyle AV}$ ${\displaystyle AB}$ ${\displaystyle C'}$ ${\displaystyle BC}$ ${\displaystyle A'}$ ${\displaystyle AC}$ ${\displaystyle B'}$ ${\displaystyle V'}$

The sentence is named after the physicist James Clerk Maxwell (1831–1879), who proved it in the context of his work on so-called reciprocal figures , which are important in statics .

literature

• Daniel Pedoe : Geometry: A Comprehensive Course . Dover, 1970, pp. 35-36, 114-115
• Daniel Pedoe: On (what should be) a Well-Known Theorem in Geometry . The American Mathematical Monthly, Vol. 74, No. 7 (Aug-Sep, 1967), pp. 839-841 ( JSTOR )
• Dao Thanh Oai, Cao Mai Doai, Quang Trung, Kien Xuong, Thai Binh: Generalizations of some famous classical Euclidean geometry theorems . International Journal of Computer Discovered Mathematics, Volume 1, No. 3, pp. 13-20

Web links

Commons : Maxwell's theorem  - collection of images, videos and audio files

• Maxwell's Theorem on cut-the-knot.org