[math-fun] (HSM) Donald Coxeter
Sad news. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Coxeter.html Dear mathematical colleagues of Donald Coxeter, It is with great sadness that I have to tell you that on March 31, 2003 Donald passed away peacefully at is home in Toronto at the age of 96. His daughter Susan was at his side as she has been since the death of his beloved wife Rien. Respecting Donald's wishes, there will be no funeral or memorial service, but cremation with only son and daughter present. Family requests not to send any flowers but instead to reflect upon Donald's long and productive life. Rather than dwell in sadness, his death should be a catalyst for people to remember the wonderful things in life and enjoy the life the way he would have wanted it. Susan would like to share with you a recent photo of Donald with his youngest great-grandchild. The bumper sticker encourages us to celebrate Donald's life. I lost a mentor, we lost a colleague, the world lost a mathematician. Asia Ivic Weiss
A few weeks ago, Serhiy Grabarchuk sent me a problem involving matchstick snakes. The object is to find the longest snake that fits inside a certain area, without ever touching or crossing over itself. Like all great problems, I initially dismissed it. My first thought was that an infinite snake could be made, but then I reread his careful rule specification ... the angles the snake could bend at were limited. Recently, I started looking at the snakes bounded by a 2x2 square, and where all angles were multiples of 30 degrees. A lot of people, including me, spent some time studying these snakes, and many unexpected solutions popped up. One person, Susan Hoover, trounced all the rest of us with a delightful length 20 snake. As a puzzle, in a 2x2 square, put 20 matchsticks end to end so that all angles between two matchsticks are multiples of 30 degrees, and so that each matchstick only touches only those matches directly before or after it in the snake. I have the solution at my site. My own best solution was a 15-length snake. Some of my better solvers sent 17-length snakes, and then a few length 19 solutions trickled in. I have already started looking at other degree multiples, and other bounding areas. This looks like a rich problem. I haven't the foggiest idea what size of 20-degree snake will fit into a radius 2 circle, but I want to know. --Ed Pegg Jr, www.mathpuzzle.com
In June 2000, Andrea Gilbert made a maze of sorts based on the Game of Life. My small part was to name the moving item the intelligent cell. The Game Of Life operates as normal, except that the Intelligent Cell may shift its position one space at the end of each cycle. Dr. William Paulsen did a large scale analysis of what an Intelligent cell could do. The results are at http://www.clickmazes.com/life/_glide3.htm . Among his discoveries is that an intelligent cell in the Loaf position can build a glider gun in 247 generations. Gliders, Eaters, and spaceships can all be built in less than 20 generations. --Ed Pegg Jr, www.mathpuzzle.com
Ed Pegg Jr <ed@mathpuzzle.com> wrote on 8 Apr 2003:
Serhiy Grabarchuk sent me a problem involving matchstick snakes [...]
Did you know that the UnaBomber enjoyed playing with matches? Below is one of his problems. A Match Stick Problem, Mathematics Magazine, Jan-Feb 1971 p.41 http://links.jstor.org/sici?sici=0025-570X(197101)44:1<41:PAS> 787. Proposed by T. J. Kaczynski, Lombard, Illinois Suppose we have a supply of matches of unit length. Let there be given a square sheet of cardboard, n units on a side. Let the sheet be divided by lines into n^2 little squares. The problem is to place matches on the cardboard in such a way that: a) each match covers a side of one of the little squares, and b) each of the little squares has exactly two of its sides covered by matches. (Matches are not allowed to be placed on the edge of the cardboard.) For what values of n does the problem have a solution? Solutions: Richard A. Gibbs: invokes Pick's theorem Richard L. Breisch: solves m by n generalization Math. Mag v.44 #5 Nov-Dec 1971 p.294 http://links.jstor.org/sici?sici=0025-570X(197111)44:5<294:PAS> Thomas Wray: solves n-dim generalization (match -> n-1 dim cube) Math. Mag. v.45 #2 Mar-Apr 1972 p.110 http://links.jstor.org/sici?sici=0025-570X(197203)45:2<110:PAS> -Bill Dubuque
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Bill Dubuque -
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Ed Pegg Jr