Showing papers on "Fibonacci number published in 1969"
Book•
01 Jan 1969
TL;DR: Hoggatt as discussed by the authors presented a 92-page booklet in its Enrichment Series entitled "Fibonacci and Lucas Numbers" by V. E. Hoggatt.
Abstract: Houghton Mifflin Company has just released a 92-page booklet in its Enrichment Series entitled "Fibonacci and Lucas Numbers" by our Editor, V. E. Hoggatt, J r . If a first impression is valid, this contribution to mathematical literature might be characterized by three words: richness, variety, lucidity. Richness and variety are manifest in relating the Fibonacci and Lucas numbers to many interesting facets of mathematics. The Golden Section Ratio and some unusual geometry receive attention in the early part of the book. Number theory comes into play in the periodic properties of the Fibonacci and Lucas numbers. The prolific Pascal triangle receives its share of attention. The algebra of simple matrices and representation of integers open up many doors to further research and study. Finally, relations with nature round off the treatment and point to the mysterious connection of mathematics with the real world which has fascinated man for untold centuries. Some examples of lucidity would be the very slick way in which the Binet formulas are introduced; the handling of asymptotic ratios and their relation to the Golden Section in Chapters 5 and 6; the treatment of periodicity of remainders in Chapter 8; the explanation of Fibonacci numbers in nature in Chapter 13. A helpful feature of the book is an appendix giving solutions of many of the problems in the book. This book should prove a boon to young and old who wish to enter that magic door which leads to the wonderful world of Fibonacci. All too often we receive pleas for books and materials dealing with this field. There is now a ready answer to these requests for help. This booklet l ists for $1.40, and is also available from the Fibonacci Association.
285 citations
16 citations
TL;DR: In this article, an explicit expression (14) for the number of p -combinations satisfying the conditions k≤d j ≤k′, j = 1(1) p −1, l≤n−d≤l′ was given.
14 citations
01 Oct 1969
TL;DR: In this article, simple formulas for quick and easy calculation of the transfer characteristics of a specific kind of ladder network have been developed starting from the Fibonacci relationship of the network.
Abstract: Simple formulas for quick and easy calculation of the transfer characteristics of a specific kind of ladder network have been developed starting from the Fibonacci relationship of the network. Examples calculating the characteristics are also given.
2 citations