Giovanni Fagnano

Giovanni Francesco Fagnano dei Toschi was an Italian churchman and mathematician, born on 31 January 1715 in Senigallia and dead there on 14 May 1797, the son of Giulio Carlo de' Toschi di Fagnano, also a mathematician. He was ordained as a priest, became a canon in 1752 and in 1755 was appointed archdeacon of the cathedral of Senigallia. In mathematics he is known for Fagnano's problem, the problem of inscribing a minimum-perimeter triangle within an acute triangle. As Fagnano showed, the solution is the orthic triangle, whose vertices are the points where the altitudes of the original triangle cross its sides. Another property of the orthic triangle, also proven by Fagnano, is that its angle bisectors are the altitudes of the original triangle.