At Knuth's site he has posted previews of forthcoming A of CP chapters --- that entitled "fasc1a" contains a discussion of exactly this subject on pp 36-39, which cites F. Herrman & M. Margenstern, Theoretical Comp. Sci. vol 296 pp. 345--351 (2003). The tiling is originally by regular pentagons meeting in fours at their vertices. The naming system in the book assigns to each cell a unique pair of integers, one of which when encoded in signed Fibonacci base permits easy computation of the names of neighbouring cells. I suspect that the other integer can be dispensed with, by naming fundamental triangles rather than entire pentagons: maybe this improvement was described in his lecture? Fred Lunnon On 8/7/07, James Propp <jpropp@cs.uml.edu> wrote:
Did anyone go to Knuth's talk at MathFest this past weekend?
It sounded interesting, but I wasn't able to go and couldn't find a write-up on the web; I'm hoping one of you can summarize.
Here's what's on the web:
PI MU EPSILON J. SUTHERLAND FRAME LECTURE
NEGAFIBONACCI NUMBERS AND THE HYPERBOLIC PLANE
Donald E. Knuth, Stanford University, Professor Emeritus of the Art of Computer Programming
Saturday, August 4, 8:00 pm - 8:50 pm
All integers can be represented uniquely as a sum of zero or more "negative" Fibonacci numbers F-1 = 1, F-2 = -1, F-3 = 2, F-4 = -3, provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles, where each triangle has one 90 degree angle, one 45 degree angle, and one 36 degree angle.
Jim Propp