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Fagnano problem

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2010 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.

References

How to Cite This Entry:
Fagnano problem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Fagnano_problem&oldid=42288
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article