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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
References
-
^ Lester, June A. (1997), "Triangles. III. Complex triangle functions",
Aequationes Mathematicae, 53 (1–2): 4–35,
doi:
10.1007/BF02215963,
MR
1436263,
S2CID
119667124
-
^
Kimberling, Clark (1996), "Lester circle", The Mathematics Teacher, 89 (1): 26,
JSTOR
27969621
-
^ Shail, Ron (2001), "A proof of Lester's theorem", The Mathematical Gazette, 85 (503): 226–232,
doi:
10.2307/3622007,
JSTOR
3622007,
S2CID
125392368
-
^ Rigby, John (2003), "A simple proof of Lester's theorem", The Mathematical Gazette, 87 (510): 444–452,
doi:
10.1017/S0025557200173620,
JSTOR
3621279,
S2CID
125214460
-
^ Scott, J. A. (2003), "Two more proofs of Lester's theorem", The Mathematical Gazette, 87 (510): 553–566,
doi:
10.1017/S0025557200173917,
JSTOR
3621308,
S2CID
125997675
-
^ Duff, Michael (2005), "A short projective proof of Lester's theorem", The Mathematical Gazette, 89 (516): 505–506,
doi:
10.1017/S0025557200178581,
S2CID
125894605
-
^ Dolan, Stan (2007), "Man versus computer", The Mathematical Gazette, 91 (522): 469–480,
doi:
10.1017/S0025557200182117,
JSTOR
40378420,
S2CID
126161757
-
^ Trott, Michael (1997),
"Applying GroebnerBasis to three problems in geometry", Mathematica in Education and Research, 6 (1): 15–28
External links