Subject: Re: [HM] Malfatti's problem
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Tue Mar 21 2000 - 07:12:20 EST
Kotera Hiroshi wrote:
> In 1803, G.F.Malfatti proposed the problem of cutting three right
> circular cylinders and of maximum total volume from a given right
> triangular prism. The problem was intuitively reduced to the
> following:
> To inscribe three circles in a given triangle so that each circle
> will be tangent to two sides of the triangle and to the other two
> circles.
>
> In "A Survey of Geometry", H.Eves said that Malfatti gave a prolix
> and incomplete analytical solution of the reduced problem.
>
> I have two questions on the Malfatti problem.
> (1)On the intuitive reduced problem, I would like to know the
> incomplete proof by Malfatti himself.
I don't know which is H. Eves' source, but mine doesn't say that Malfatti's
solution was wrong.
F.G.-M. (Exercices de geometrie..., p. 727) writes:
La solution (i>tres simple</i>, donnee par MALFATTI, a ete communiquee
aux Annales, mais sans demonstration, par BIDONE, professeur a l' Academie
de Turin (tome I, p. 347).
>(2)Is the original Malfatti problem still unsolved?
No. It is solved. See:
Zalgaller, V.A. - Los', G.A.: The Solution of Malfatti's Problem.
J. Math. Sci., New York 72:4 (1994), 3163-3177
(Translation from Ukr. Geom. Sb. 35(1992) 14-33)
Martini, Horst: Recent Results in Elementary Geometry. II.
Behara, Minaketan (ed.) et al.: Proceedings of the 2nd Gauss
Symposium. Conference A: Mathematics and Theoretical Physics, Munich,
Germany, August 2-7, 1993. Berlin: Walter de Gruyter. Symposia Gaussiana.
419-443 (1995). [ISBN 3-11-014476-X/hbk]
Antreas
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