Problem 221. Viviani's Theorem, Equilateral Triangle,
Point, Altitude, Distance
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In an equilateral triangle, prove that the sum of the distances from any interior point to the sides is equal to the altitude of the triangle.
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The theorem is named for Vincenzo Viviani (1622-1703), a pupil of Galileo and Torricelli, who is also remembered for a reconstruction of a book on the conic sections of Apollonius and for finding a way of trisecting an angle through the use an equilateral hyperbola.
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