Fagnano's problem [SEP] named after
Fagnano's problem
In geometry, Fagnano's problem is an optimization problem that was first stated by Giovanni Fagnano in 1775:
The solution is the orthic triangle, with vertices at the base points of the altitudes of the given triangle.
Solution.
The orthic triangle, with vertices at the base points of the altitudes of the given 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
pp. 88–89.
- H.A. Schwarz: "Gesammelte Mathematische Abhandlungen, vol. 2". Berlin 1890, pp. 344-345. (online at the Internet Archive, German)
External links.
- Fagnano's problem at cut-the-knot
- Fagnano's problem in the Encyclopaedia of Mathematics
- Fagnano's problem at a website for triangle geometry