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The Fermat Point of Triangles: A Correction

The Fermat Point of Triangles: A Correction

1. Introduction Previously, I had written a post detailing the Fermat point of a triangle: the unique point which minimizes the sum of distances to the triangle’s vertices. Recently, I realized a small oversight I had made in my proof of the case where all of the triangle’s angles are less than . In today’s post, we will be patching this oversight, so it is recommended to read through the original post before continuing (as a challenge, try to find…

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Small Displacements Revisited: The Fermat Point

Small Displacements Revisited: The Fermat Point

1. Introduction This post will continue my investigation into the “method” of small geometrical displacements that I discussed in my previous post. I will apply it to a famous problem regarding triangles: the Fermat point. The Fermat point of a triangle is defined as the point in the plane of the triangle that minimizes the sum of the distances to each of the vertices. As we learned in the last post, the method of small displacements can be very useful…

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