There's a much simpler question: what's the smallest number of pieces for dissecting a square into (pieces that can be rearranged to form) an equilateral triangle? 4 is possible - see http://oeis.org/A110312, especially the last link. 3 seems impossible, but is there a proof? The pieces must be bounded by simple curves. Neil On Thu, Sep 26, 2013 at 10:47 PM, Victor Miller <victorsmiller@gmail.com>wrote:
Scott, this is discussed (rather tersely) here: http://www.ics.uci.edu/~eppstein/junkyard/cube-triangulation.html . Also, if you don't know about David Eppstein's Geometry Junkyard, you should. It's a treasure trove of all sorts of wonderful things:
http://www.ics.uci.edu/~eppstein/junkyard
Victor
On Thu, Sep 26, 2013 at 8:51 PM, <rcs@xmission.com> wrote:
This is from Scott Huddleston <scott.huddleston@intel.com> --Rich ---
What's the minimum number of pieces for dissecting an n-cube into n-simplices? You can always dissect into n! simplices, but that's not minimal for n>2.
This was an open problem when I was in grad school (awhile back).
Is there always a minimal dissection that includes a maxvol simplex?
- Scott
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-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com