# calculate Fermat Point

Version 1.0.1 (2.82 KB) by
Returns the first Fermat point of a triangle with vertices (A,B,C).
Updated 19 Jun 2023

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, atbecker@uh.edu 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.

### Cite As

Aaron T. Becker's Robot Swarm Lab (2024). calculate Fermat Point (https://www.mathworks.com/matlabcentral/fileexchange/131254-calculate-fermat-point), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2023a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux