GEOMETRY A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z                    HOME ABOUT CATEGORIES SITE MAP COPYRIGHT ADVERTISE CONTACT entire Web this site Fagnano's problem Solution to Fagnano's problem Image source: J. Wilson, Univ. of Georgia In a given acute triangle ABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of ABC, that is, the triangle (DEF) whose vertices are endpoints of the altitudes from each of the vertices of ABC. The problem was proposed and solved using calculus by Giovanni Fagnano (1715–1797) in 1775. Once the answer became known, several purely geometric solutions were also discovered. Related category    • GEOMETRY Also on this site: Encyclopedia of Alternative Energy & Sustainable Living Encyclopedia of History Transport Concepts & Designs (partner site) BACK TO TOP