The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Brian Chandler

Posts: 1,899
Registered: 12/6/04
Re: smallest containing cube
Posted: Oct 2, 2012 2:33 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.