First Fermat Point


The first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances from A, B, and C in an acute triangle,


It has equivalent triangle center functions


and is Kimberling center X_(13) (Kimberling 1998, p. 67).

It also arises in Napoleon's theorem.

See also

Fermat Axis, Fermat Points, Napoleon's Theorem, Second Fermat Point

Explore with Wolfram|Alpha


Kazarinoff, N. D. Geometric Inequalities. New York: Random House, pp. 117-118, 1961.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Fermat Point.", C. "Encyclopedia of Triangle Centers: X(13)=1st Isogonic Center."

Referenced on Wolfram|Alpha

First Fermat Point

Cite this as:

Weisstein, Eric W. "First Fermat Point." From MathWorld--A Wolfram Web Resource.

Subject classifications