A·
C· ·B
Pierre de Fermat first gave the problem, "Find the point in a triangle where the sum of its distances to the three vertices is minimal".
Torricelli is credited with being the first to find a solution to this problem.
Torricelli's Method Begins by making the
equilateral triangle of 2 of the 3 points and X, where angle AC intersects XC at C, and AB intersects XB at B.
A·
C· ·B
·X
Circumscribe a circle containing points C, B, and X (no, i'm not about to try and draw all of this in
ascii).
A·
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C·` `·B
·X
Point S exists where line AX intersects the circle containing points CBX.
A·
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_.--·"¯ ¯"`._
C·` \S `·B
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·X