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Math Forum » Discussions » sci.math.* » sci.math

Topic: smallest containing cube
Replies: 25   Last Post: Oct 5, 2012 11:59 AM

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Brian Chandler

Posts: 1,899
Registered: 12/6/04
Re: smallest containing cube
Posted: Oct 2, 2012 2:33 AM
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Tim Little wrote:
> On 2012-10-01, quasi <quasi@null.set> wrote:
> > Let C be a cube in R^3 and suppose S is a subset of C such that
> > each (closed) face of C contains at least one point of S.
> >
> > Prove or disprove:
> >
> > Of all cubes that contain S, C has the least volume.
>
> Disproof: Let S = intersection of unit cube centered at the origin
> with the coordinate axes. There is a smaller cube that contains S;
> one that is not aligned with the coordinate axes.

Seems plausible, but not obvious. Can you show the explicit such
smaller cube?

Brian Chandler

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