Games For Arbitrarily Fat Rats
Workshop on Combinatorial Games, in honor of Elwyn Berlekamp's 75th Birthday November 01, 2015 - November 02, 2015
Location: SLMath: Eisenbud Auditorium
Tags/Keywords
Diophantine approximation
fat rats
Dedekind cut
Wythoff's game
subtraction game
05-02 - Research exposition (monographs, survey articles) pertaining to combinatorics
05-06 - Proceedings, conferences, collections, etc. pertaining to combinatorics
14405
In kindergarten we learned about the integers (Peano axioms); in gram-
mar schhol { about pairs of integers (rationals); and then in high school,
about the reals (Dedekind cuts). Berlekamp, Conway, Guy discovered and
promoted a method (Don Knuth: \Surreal Numbers") of creating all of
those and much more { namely games! { in one masterful stroke.
Yet the rationals sometimes present obstinate diculties often over-
looked. Example. Let 1 < 1 <; : : : ;< m be real numbers, dubbed moduli ,
m 3. An over 40 years old conjecture states that there exist reals
i such
that the system (bn1 +
1c; : : : ; bnmc +
mc) constitutes a complemen-
tary system of m sequences of integers if and only if i = (2m
14405
H.264 Video |
14405.mp4
|
Download |
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.