Counting the Angels and Devils in Escher's Circle Limit IV

Journal of Humanistic Mathematics

Pippenger, Nicholas¹  Choi, John² 

[1]Harvey Mudd College

关键词: Tessellations;    enumerative combinatorics;   

DOI  :  10.5642/jhummath.201502.05

学科分类：卫生学

来源: Cleveland Clinic Educational Foundation

【 摘 要 】

We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).

【 授权许可】

Unknown