The golden ratio and Fibonacci numbers. (English) Zbl 0968.11013
Singapore: World Scientific. vii, 162 p. (1997).
There are numerous books on the golden ratio and related topics, ranging from philosophical via geometric to rather number theoretical expositions.
The present book is a welcome addition: It is elementary and illustrative (hence readable with school knowledge), but it also addresses many applications. The latter range from geometry via some elementary number theory to search algorithms, Penrose tilings and quasicrystals, and to biological applications.
This volume can serve as a convincing illustration of the fact that interesting mathematical structures keep reappearing over and over again – and that it is thus a good idea to study them in their own right.
The present book is a welcome addition: It is elementary and illustrative (hence readable with school knowledge), but it also addresses many applications. The latter range from geometry via some elementary number theory to search algorithms, Penrose tilings and quasicrystals, and to biological applications.
This volume can serve as a convincing illustration of the fact that interesting mathematical structures keep reappearing over and over again – and that it is thus a good idea to study them in their own right.
Reviewer: M.Baake (Tübingen)
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 11-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory |
| 97-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education |
Online Encyclopedia of Integer Sequences:
Decimal expansion of golden ratio phi (or tau) = (1 + sqrt(5))/2.Minimal (or ”greedy”) Lucas representation of n, in which L(0) = 2 and L(2) = 3 are not allowed in the same representation (hence the correct representation of the integer 5 is 1010 rather than 101). A binary system of integers with Lucas numbers (A000032) as a base.
