Fagnano problem

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2020 Mathematics Subject Classification: Primary: 51M04 Secondary: 51-0301A50 [MSN][ZBL]

The problem in which one is required to inscribe a triangle of least possible perimeter in a given acute-angled triangle. The solution is the orthocentric triangle, that is, the triangle whose vertices are the feet of the altitudes of the given triangle. The problem was posed by G. Fagnano dei Toschi in 1775.


  • H. S. M. Coxeter, S. L. Greitzer, "Geometry Revisited", Mathematical Association of America (1967) ISBN 0883856190 Zbl 0166.16402
How to Cite This Entry:
Fagnano problem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article