I was reading through Archimedes' Revenge by Paul Hoffman, and ran across an interesting comment.
It said that 153 lies dormant in every multiple of 3. Here's how: take the digits
of a (positive) multiple of 3, cube each of them and add them together. Repeat this process with the
new number (also a multiple of 3). Eventually, you will get 153.
Since 13+53+33=153, you're now
stuck at 153. Way cool, but WHY? I've been trying to prove this, and I have a clunky proof that
I'd like to share. If you have a horribly elegant proof (or just one better than mine), PLEASE share!
The Proof!
Older Stuff that I haven't had a chance (or inclination) to update:
Mathematical
I work in affine Lie Algebras. I've been studying the principal
characters of these algebras: writing a program to generate the formulas,
finding patterns in the forms, and using the patterns to construct
integrable highest weight representations. I've written a paper
describing the program and proving some of the identities I've found
using this program. It will soon appear in Mathematics of Computation.
My mathematical
publications are:
-
"Level two representations of $A_{7}^{(2)}$ and the Rogers-Ramanujan Identities",
Communications in Algebra, 1994 (with K. Misra).
-
"An Application of Crystal Bases to Representations of Affine Lie Algebras",
Journal of Algebra, 1995 (with K. Misra).
Pedagogical
I've been working on TOTI
(teaching with on-line technologies) and Women
and Science Literacy Grant. For TOTI, I've been working on expanding
communication between myself and my students through the Web. My pedagogical
publication is:
-
"Improving Computer Literacy in a Math Classroom for Non-Math Majors,"
The Journal of Computing in Small Colleges, Proceedings of the Second Annual
CCSC Northeastern Conference, 1997.
The Women and Science Literacy Grant seeks to expand the content and pedagogies
of the undergraduate science and math curriculum as well as the
humanities.
I'm also currently a member of PKAL Faculty 21.