Malfatti circles

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Construct three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle.

[edit] History

In 1803 Gian Francesco Malfatti thought that solving this problem would also provide a solution to Malfatti's problem. However in 1930, it was shown that the Malfatti circles were not always the best solution. Then in 1967 Goldberg showed that, even worse, they are never the best solution (Ogilvy 1990). Ogilvy (1990) and Wells (1991) then illustrated specific cases where alternative solutions are clearly optimal.

[edit] External links

[edit] References

  • Dörrie, H. "Malfatti's Problem." §30 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 147-151, 1965. ISBN 0-486-61348-8
  • Goldberg, M. "On the Original Malfatti Problem." Math. Mag. 40, 241-247, 1967.
  • Ogilvy, C. S. Excursions in Geometry. New York: Dover, 1990. ISBN 0-486-26530-7
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