High Quality Content by WIKIPEDIA articles! In geometry, Fagnano's problem is an optimization problem that was first stated by Giovanni Fagnano in 1775The orthic triangle has the smallest perimeter of all triangles inscribed into an acute triangle, hence it is the solution of Fagnano's problem. Fagnano's original proof used calculus methods and an intermediate result given by his father Giulio Carlo de' Toschi di Fagnano. Later however several geometric proofs were discovered as well, amongst others by Hermann Schwarz and Lipot Fejer. These proofs use the geometrical properties of reflections to determine some minimal path representing the perimeter.

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