{"product_id":"the-golden-ratio-and-fibonacci-richard-a-dunlap-9789810232641","title":"The Golden Ratio and Fibonacci Numbers","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Richard A. Dunlap\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9810232640\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789810232641\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/17\/1997\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 172\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.93lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 8.63h x 6.24w x 0.71d","brand":"Richard A. Dunlap","offers":[{"title":"Hardcover","offer_id":43941381341439,"sku":"9789810232641","price":62.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_858e7ec9-cce7-455f-819a-41769456bb4c.jpg?v=1681452593","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-golden-ratio-and-fibonacci-richard-a-dunlap-9789810232641","provider":"WR Book House","version":"1.0","type":"link"}