Maxwell's theorem (geometry)

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 .

Line segments with identical markings are parallel.
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

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 (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
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