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Pólya's Mechanical Model for the Fermat Point
Pólya's Mechanical Model for the Fermat Point
The Fermat point (also called Torricelli point) is the point inside a triangle (provided no angle exceeds 120 degrees) such that the sum of its distances from the vertices is a minimum.
Three strings are attached to a ball and passed through holes in a horizontal table, with equal weights attached at the ends of the strings under the table. Then the ball is at the Fermat point.
One of the holes can be shifted. As the hole moves the ball's position changes, constantly keeping the strings aligned at 120 degrees.
This model serves as an interesting (and rare) example in which a geometric theorem is proved by means of physical principles.