Re: Sphere inside a pyramid


Timothy Little wrote:
> matt271829-news@xxxxxxxxxxx wrote:
> > Timothy Little wrote:
> >> Consider cones with apex coinciding with that of the pyramid. If a
> >> sphere can be inscribed in the pyramid, the cone that encloses the
> >> sphere will intersect the base in a circle that touches the edges.
> >
> > How do you know it's a circle? It's more likely to be an ellipse
> > isn't it?
>
> Oops. Yes, that's true and makes the conjecture false.
>
> For example, a square pyramid with slanted base can have a sphere
> inscribed, but the base is a non-square rectangle.

Yeah, sort of, except I think you'll find that the base won't be
rectangular... it will be some sort of trapezium at best.

.

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