Fermat Point

AP =	2.00	angle APB =	135.00	°
BP =	3.54	angle APC =	135.00	°
CP =	3.54	angle BPC =	90.00	°
AP+BP+CP =	9.07	angle AFB =	120.00	°
AF+BF+CF =	8.83	angle AFC =	120.00	°
		angle BFC =	120.00	°

The Fermat point

F

minimizes the sum of the distances from

F

to the vertices of an acute triangle. In an acute triangle, the angle formed by the segments connecting any two vertices with

F

is 120 degrees. Also, if one forms an equilateral triangle using two of the vertices of the original triangle, the third vertex of the equilateral triangle lies on a line through

F

and the third vertex of the original triangle. These equilateral triangles are shown in gray.

External Links

First Fermat Point (Wolfram MathWorld)

Permanent Citation

Chris Boucher

"Fermat Point"
http://demonstrations.wolfram.com/FermatPoint/
Wolfram Demonstrations Project
Published: September 28, 2007