Re: Sphere inside a pyramid

Don Taylor <dont@xxxxxxxxxxxxxxx> writes in article <29mdnYozn8UYOrHeRVn-qA@xxxxxxxxxxxxxxx> dated Sat, 17 Sep 2005 18:32:21 -0500:
>"odin" <ragnarok@xxxxxxxxx> writes:
>>>> What is the equation of the sphere inside a pyramid of unequal sides such
>>>> that each surface of the pyramid is tangent to the sphere?

The equation, of course, is (x-x0)^2+(y-y0)^2+(z-z0)^2=r^2

>>> In general there won't be one.
>
>>True. It would be like asking what circle fits in an arbitrary rectangle
>>such that each side is a tangent to the circle. Only squares work.
>
>But the original poster didn't really specify that the "pyramid"
>was made up of five faces.
>
>With 4 faces, i.e. a tetrahedron, it seems like he can satisfy the
>conditions, for any arbitrary triangular faces. And I might even
>suspect the solution would be a generalization of inscribing a
>circle inside a triangle.

True or false: A sphere can be inscribed in a pyramid IFF a circle can be
inscribed in its base.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

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