Fagnano's Problem


In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was proposed and solved using calculus by Fagnano in 1775 (Coxeter and Greitzer 1967, p. 88).

See also

Acute Triangle, Orthic Triangle, Perimeter

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Bogomolny, A. "Fagnano's Problem: What Is It?", H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 21, 1969.Coxeter, H. S. M. and Greitzer, S. L. "Fagnano's Problem." §4.5 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 88-89, 1967.Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 347, 1996.Ha, N. M. "Another Proof of Fagnano's Inequality." Forum Geom. 4, 199-201, 2004., N. D. Geometric Inequalities. New York: Random House, pp. 76-77, 1961.Morley, F. and Morley, F. V. Inversive Geometry. Boston, MA: Ginn, p. 37, 1933.

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Fagnano's Problem

Cite this as:

Weisstein, Eric W. "Fagnano's Problem." From MathWorld--A Wolfram Web Resource.

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