Subject: Re: [HM] Malfatti's problem
From: John Conway (conway@math.Princeton.EDU)
Date: Wed Mar 22 2000 - 21:46:12 EST
On Tue, 21 Mar 2000, Antreas P. Hatzipolakis wrote:
>
> 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.
Let's call this problem (1).
> > 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.
Let's call this problem (2).
> I don't know which is H. Eves' source, but mine doesn't say that Malfatti's
> solution was wrong.
What Malfatti did correctly was to solve problem (2). But
this doesn't happen to give the solution to problem (1), for which
the incircle is one of the 3 circles involved. Get it??
John Conway
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