calculate Fermat Point

Returns the first Fermat point of a triangle with vertices (A,B,C).

calculateFermatPoint(A,B,C) returns the first Fermat point of a triangle with vertices (A,B,C).

https://wikipedia.org/wiki/Fermat_point: "In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible[1] or, equivalently, the geometric median of the three vertices. It is so named because this problem was first raised by Fermat in a private letter to Evangelista Torricelli, who solved it."

This implementation was based off the Mathematica code by E. Coiras at:https://demonstrations.wolfram.com/FirstFermatPointAndIsogonicCenterOfATriangle/

Aaron Becker, [e-mail] and David Kramer

Last updated June 17, 2023

testCalculateFermatPoint.m Generates and plots a random triangle and the First Fermat Point. It tests the function calculateFermatPoint(A,B,C)

The vertex angles are less than 120° the First Fermat Point is in the interior of the triangle; otherwise it is the obtuse-angled vertex.

[1] "Cut The Knot - The Fermat Point and Generalizations" http://www.cut-the-knot.org/Generalization/fermat_point.shtml