--- product_id: 51064519 title: "GOLDEN RATIO AND FIBONACCI NUMBERS, THE" price: "€ 113.75" currency: EUR in_stock: true reviews_count: 5 url: https://www.desertcart.pt/products/51064519-golden-ratio-and-fibonacci-numbers store_origin: PT region: Portugal --- # GOLDEN RATIO AND FIBONACCI NUMBERS, THE **Price:** € 113.75 **Availability:** ✅ In Stock ## Quick Answers - **What is this?** GOLDEN RATIO AND FIBONACCI NUMBERS, THE - **How much does it cost?** € 113.75 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.pt](https://www.desertcart.pt/products/51064519-golden-ratio-and-fibonacci-numbers) ## Best For - Customers looking for quality international products ## Why This Product - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Description "This attractive and carefully written book addresses the general reader with interest in mathematics and its application to the physical and biological sciences ... this one will make a valuable addition to academic and personal libraries." The Fibonacci Quarterly In this invaluable book, 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 Fibonacci 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, lattice 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. Review: The definitive book on the subject - This book is not absolutely perfect, but it is so much better than any other one on the subject that it deserves a 5-star rating. The majority of books on Fibonacci numbers and the golden ratio fall into three categories: (1) Books for children, (2) Mystical mumbo-jumbo, and (3) Books claiming you can use Fibonacci numbers to win in the stock market (!). Even Mario Livio's book, which is better than most, uses so much of its space to _debunk_ some of the mystical mumbo-jumbo that it de-emphasizes the wonderful patterns that can be found in the Fibonacci sequence, which is beautiful enough in its mathematical properties that one doesn't need to make such digressions. Dunlap's book, by contrast, _does_ emphasize those patterns. And when it's not directly addressing the Fibonacci sequence's properties, it's discussing things like the golden ratio and Penrose tilings, which are completely within the category of mathematics related to the topic. I really enjoyed the book, even though it has some typographical errors and minor omissions. The formulas collected in the third appendix alone justify buying the book. I could wish that there were more given, but this is the best collection I have seen. Review: Four Stars - Ok ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #3,171,597 in Books ( See Top 100 in Books ) #634 in Number Theory (Books) #1,308 in Geometry #2,472 in Geometry & Topology (Books) | | Customer Reviews | 4.6 out of 5 stars 6 Reviews | ## Images ![GOLDEN RATIO AND FIBONACCI NUMBERS, THE - Image 1](https://m.media-amazon.com/images/I/716jBjgZRZL.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ The definitive book on the subject *by B***N on February 2, 2006* This book is not absolutely perfect, but it is so much better than any other one on the subject that it deserves a 5-star rating. The majority of books on Fibonacci numbers and the golden ratio fall into three categories: (1) Books for children, (2) Mystical mumbo-jumbo, and (3) Books claiming you can use Fibonacci numbers to win in the stock market (!). Even Mario Livio's book, which is better than most, uses so much of its space to _debunk_ some of the mystical mumbo-jumbo that it de-emphasizes the wonderful patterns that can be found in the Fibonacci sequence, which is beautiful enough in its mathematical properties that one doesn't need to make such digressions. Dunlap's book, by contrast, _does_ emphasize those patterns. And when it's not directly addressing the Fibonacci sequence's properties, it's discussing things like the golden ratio and Penrose tilings, which are completely within the category of mathematics related to the topic. I really enjoyed the book, even though it has some typographical errors and minor omissions. The formulas collected in the third appendix alone justify buying the book. I could wish that there were more given, but this is the best collection I have seen. ### ⭐⭐⭐⭐ Four Stars *by A***R on February 10, 2016* Ok ### ⭐⭐⭐⭐⭐ This was exactly what I expected *by D***I on February 6, 2012* I wanted a book that was concerned on nature observations, but much more on mathematical demonstrations, equations and formulas. The book have been perfect in this sense! So, if you want to understand the numerical and geometrical relations from Fibonacci Numbers, this book is a good start. --- ## Why Shop on Desertcart? - 🛒 **Trusted by 1.3+ Million Shoppers** — Serving international shoppers since 2016 - 🌍 **Shop Globally** — Access 737+ million products across 21 categories - 💰 **No Hidden Fees** — All customs, duties, and taxes included in the price - 🔄 **15-Day Free Returns** — Hassle-free returns (30 days for PRO members) - 🔒 **Secure Payments** — Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** — Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.pt/products/51064519-golden-ratio-and-fibonacci-numbers](https://www.desertcart.pt/products/51064519-golden-ratio-and-fibonacci-numbers) --- *Product available on Desertcart Portugal* *Store origin: PT* *Last updated: 2026-10-05*