= Fermat point
{c}
= Torricelli point
{c}
{synonym}
A <Fermat point> of a <triangle> minimizes the sum of <Euclidean distances> to its three vertices. If every interior <angle> is less than $120^\circ$, the minimizer lies inside, and the three joining segments meet at pairwise <angles> of $120^\circ$. Indeed the <gradient> of the sum at an interior minimizer is the sum of three unit <vectors> toward the vertices; three unit <vectors> sum to zero exactly in this configuration. Convexity of distance makes this stationary point a global minimizer. If one interior <angle> is at least $120^\circ$, that vertex is a minimizer instead. For an <equilateral triangle>, the <Fermat point> is its <centroid>.
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