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שפה נוכחית
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The golden ratio and Fibonacci numbers [electronic resource]
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In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are also presented. ; In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, latice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections.;The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.
| Title |
The golden ratio and Fibonacci numbers [electronic resource] / by Richard A. Dunlap. |
|---|---|
| Publisher |
River Edge, NJ : World Scientific |
| Creation Date |
c2003, c1997 |
| Notes |
Bibliographic Level Mode of Issuance: Monograph Includes bibliographical references and index. English |
| Content |
Basic properties of the golden ratio geometric problems in two dimensions geometric problems in three dimensions Fibonacci numbers Lucas numbers and generalized Fibonacci numbers continued fractions and rational approximants generalized Fibonacci representation theorems optimal spacing and search algorithms commensurate and incommensurate projections Penrose tilings quasicrystallography biological applications construction of the regular pentagon the first 100 Fibonacci and Lucas numbers relationships involving Fibonacci and Lucas numbers. |
| Extent |
1 online resource (172p. ) illustrations |
| Language |
English |
| National Library system number |
997010703638305171 |
MARC RECORDS
Tags
- Fibonacci numbers.
- Golden section.
- Divine proportion (Mathematics)
- Divine section (Mathematics)
- Extreme and mean ratio
- Golden cut
- Golden mean (Mathematics)
- Golden number (Ratio)
- Golden proportion
- Golden ratio
- Mean of Phidias
- Medial section
- Phi ratio
- Phidias, Mean of
- Fibonacci sequence
- Numbers, Fibonacci
- Sequence, Fibonacci
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