Giovanni Francesco Fagnano dei Toschi (born 31 January 1715 in Senigallia, died 14 May 1797 in Senigallia) was an Italian churchman and mathematician, the son of Giulio Carlo de' Toschi di Fagnano, also a mathematician.
In 1752 he became canon,[1] and in 1755[1] he was appointed archdeacon of the cathedral of Senigallia.
[2] Fagnano 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.
As Fagnano showed, when the four points form the vertices of a convex quadrilateral, the geometric median is the point where the two diagonals of the quadrilateral cross each other.