Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

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

Advanced Search
Reply to this Topic Reply to this Topic

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]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.