Maxwell's theorem (geometry)
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If the sides of the triangle are parallel to the according cevians of triangle , which are intersecting in a common point , then the cevians of triangle , which are parallel to the according sides of triangle intersect in a common point as well
Maxwell's theorem is the following statement about triangles in the plane.
For a given triangle and a point not on the sides of that triangle construct a second triangle , such that the side is parallel to the line segment , the side is parallel to the line segment and the side is parallel to the line segment . Then the parallel to through , the parallel to through and the parallel to through intersect in a common point .
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
[edit]- 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 (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, Vol. 1, No. 3, pp. 13–20
External links
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Wikimedia Commons has media related to Maxwell's theorem.
- Maxwell's Theorem at cut-the-knot.org