Maxwell's theorem (geometry)

{{short description|Given a triangle and a point, constructs a second triangle with a special point}}

Maxwell's theorem is the following statement about triangles in the plane.

{{quote|For a given triangle $ABC$ and a point $V$ not on the sides of that triangle construct a second triangle $A'B'C'$ , such that the side $A'B'$ is parallel to the line segment $CV$ , the side $A'C'$ is parallel to the line segment $BV$ and the side $B'C'$ is parallel to the line segment $AV$ . Then the parallel to $AB$ through $C'$ , the parallel to $BC$ through $A'$ and the parallel to $AC$ through $B'$ intersect in a common point $V'$ .}}

The theorem is named after the physicist James Clerk Maxwell (1831–1879), who proved it in his work on reciprocal figures, which are of importance in statics.

References

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 (August – September, 1967), pp. 839–841 ([https://www.jstor.org/stable/2315813 JSTOR])
Dao Thanh Oai, Cao Mai Doai, Quang Trung, Kien Xuong, Thai Binh: [http://www.journal-1.eu/2016-3/Dao-Thanh-Oai-Generalizations-pp.12-20.pdf "Generalizations of some famous classical Euclidean geometry theorems."] International Journal of Computer Discovered Mathematics, Vol. 1, No. 3, pp. 13–20

External links

[https://www.cut-the-knot.org/Curriculum/Geometry/Maxwell.shtml Maxwell's Theorem] at cut-the-knot.org

Category:Elementary geometry

Category:Theorems about triangles

Category:James Clerk Maxwell