### GREETINGS

from

Wlodzimierz (Wlodek)
Kuperberg

Department of Mathematics & Statistics

Auburn
University

I am a faculty member
of the Department of
Mathematics and Statistics, Auburn
University.
During the current Semester (Fall 2013), I am teaching Linear Differential Equations
MATH 2650 and Discrete Geometry and Convexity I, MATH 7110. I can
can be seen in my office on Mondays, Wednesdays and Fridays at 9:00-9:50 a.m. or by appointment
made by e-mail or telephone (see below).
I can be reached by

- phone: (334)-844-6594
- FAX: (334)-844-6555
- E-mail:
kuperwl@auburn.edu
- Paper mail:

Department of Mathematics

Auburn University

Auburn, AL 36849-5310

My interests in mathematics are
GEOMETRY and
TOPOLOGY.
Click on either one of the two to see the list of my publications on the
topic.

### A PROBLEM IN GEOMETRY

**Here is a problem in geometry:** What is the minimum number of unit
cubes in d dimensions which can cover a larger cube? For example, three unit
squares (in the plane) can cover a larger square, but two cannot. It is
not hard to show that d+1 unit d-cubes can cover a larger d-cube, but is
d+1 the smallest number possible? If you can answer this question, even
in some special cases, please write to me about it.

`
By the way, a similar question can be asked about other solids in place
of the cube. The d-ball is an interesting, yet fairly easy, example:
`

` THEOREM:`* The smallest number of unit* d*-balls that can
cover a larger *d*-ball is *d+1.

` The proof can be
assigned to geometry students as a nice exercise.`

### UNBELIEVABLE STUFF!

Despite my relatively old age (I am well over 40), I have recently
won a
### FIELDS MEDAL!!!

If you don't believe me,
see
for yourself!

### Thank you for dropping in to this site and come back to visit again
sometime!

DISCLAIMER. All and any (if any) views, opinions, statements of fact,
jokes, etc., expressed on this Web page are solely those of the individual
named and pictured above, and not necessarily of the Department of
Mathematics, Auburn University, or any other institution or individual. A
hard copy of this disclaimer, signed and sealed in the presence of a
Notary Public, is being kept locked in a safe vault at an undisclosed
location.

COPYRIGHT WARNING. Any unauthorized copying of the material included in this
page or any portion thereof for monetary gain or other form of profit is
stricly prohibited and will be prosecuted to the full extent of the law,
although I can hardly imagine anyone foolish enough to attempt to gain a
single penny by doing so in the first place. (This warning too is covered by
the very same warning!)

##### * Page last updated on August 23, 2013 *