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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry the Fermat point of a triangle, also called Torricelli point, is the solution to the problem of finding a point such that the total distance from the three vertices of the triangle to the point is the minimum possible. It is so named because this problem is first raised by Fermat in a private letter.Given any Euclidean triangle ABC and an arbitrary point P let d(P) = PA+PB+PC. The aim of this section is to identify a point P0 such that d(P0) d(P) for all P P0. If such a point exists then it will be the Fermat point. In what follows will denote the points inside the triangle and will be taken to include its boundary .