Re: Closed convex hull and cube
From: M.J.T. Guy (mjtg_at_cus.cam.ac.uk)
Date: 02/11/05
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Date: 11 Feb 2005 17:08:40 GMT
Timothy Little <tim-via-n.i.net@little-possums.net> wrote:
>"Gerry Myerson" <gerry@maths.mq.edi.ai.i2u4email> wrote:
>> Take a cylinder.
>> Shear it so its cross-sections are ellipses and
>> its axis is not orthogonal to its base.
>> Can you inscribe a cube in that?
>
>If we rotate it so that its axis is vertical, then it is just a
>squashed cyclinder with elliptical cross-sections in the horizontal
>planes. Inscribe a square in the cross-section, and extend it
>vertically to a cube.
That only works if the cylinder is long enough. But if the cylinder
is short enough, we can put a cube between the two end parallel end
planes.
Is there a combination of eccentricity, angle between base and axis
and length for which neither construction holds?
Mike Guy
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