Lester's theorem
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Short description: Several points associated with a scalene triangle lie on the same circle
In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle. The result is named after June Lester, who published it in 1997,[1] and the circle through these points was called the Lester circle by Clark Kimberling.[2] Lester proved the result by using the properties of complex numbers; subsequent authors have given elementary proofs[3][4][5][6], proofs using vector arithmetic,[7] and computerized proofs.[8]
See also
- Parry circle
- Shape § Similarity classes
- van Lamoen circle
References
- ↑ Lester, June A. (1997), "Triangles. III. Complex triangle functions", Aequationes Mathematicae 53 (1–2): 4–35, doi:10.1007/BF02215963
- ↑ "Lester circle", The Mathematics Teacher 89 (1): 26, 1996
- ↑ Shail, Ron (2001), "A proof of Lester's theorem", The Mathematical Gazette 85 (503): 226–232, doi:10.2307/3622007
- ↑ Rigby, John (2003), "A simple proof of Lester's theorem", The Mathematical Gazette 87 (510): 444–452, doi:10.1017/S0025557200173620
- ↑ Scott, J. A. (2003), "Two more proofs of Lester's theorem", The Mathematical Gazette 87 (510): 553–566, doi:10.1017/S0025557200173917
- ↑ Duff, Michael (2005), "A short projective proof of Lester's theorem", The Mathematical Gazette 89 (516): 505–506, doi:10.1017/S0025557200178581
- ↑ Dolan, Stan (2007), "Man versus computer", The Mathematical Gazette 91 (522): 469–480, doi:10.1017/S0025557200182117
- ↑ Trott, Michael (1997), "Applying GroebnerBasis to three problems in geometry", Mathematica in Education and Research 6 (1): 15–28, http://library.wolfram.com/infocenter/Articles/1754/
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