View source for Maxwell's theorem (geometry)

{{short description|Given a triangle and a point, constructs a second triangle with a special point}}
[[File:Maxwell theorem2.svg|thumb|upright=1.5|Line segments with identical markings are parallel.<br/> If the sides of the triangle<math>A'B'C'</math> are parallel to the according cevians of triangle <math>ABC</math>, which are  intersecting in a common point <math>V'</math>, then the cevians of triangle <math>A'B'C'</math>, which are parallel to the according sides of triangle <math>ABC</math> intersect in a common point <math>V'</math> as well]]
'''Maxwell's theorem''' is the following statement about triangles in the plane.

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

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

== References ==
* [[Biography:Daniel Pedoe|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]]

{{Sourceattribution|Maxwell's theorem (geometry)}}