{"product_id":"the-fibonacci-resonance-and-other-new-golden-ratio-discoveries-maths-music-archaeology-architecture-art-quasicrystals-metamaterials-hardcover","title":"The Fibonacci Resonance and other new Golden Ratio discoveries: Maths, music, archaeology, architecture, art, quasicrystals, metamaterials, ... - Hardcover","description":"\u003cp\u003eA new and definitive reference for the Fibonacci numbers and the Golden Ratio. With Mondrian, Seurat, Toulouse-Lautrec, Tiwanaku, The Great Pyramid, Le Corbusier, Kepler, Penrose, quasicrystals, Pendry, green energy, and the latest light-based technologies, this maths and science book is written to be enjoyed. Explore Bohemian Paris - the capital of phi - in fresh analyses of art, architecture, and music. Lavishly illustrated, this book includes: the history of Fibonacci and Lucas numbers, spirals, sunflowers, pine cones, megaliths, and ornamental tilings. The Fibonacci Resonance discovery is revealed step by step from unique beginnings to abacus-bead visualizations. Comparisons are made with Silver Ratio Pell numbers, and a link is shown to perfect numbers and record-breaking Mersenne primes.\u003c\/p\u003e","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":50156260557023,"sku":"9780993216602","price":96.12,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0813\/8958\/4607\/files\/amNxUkNBdHdIY2F3bDk1YUNYdGVyQT09.webp?v=1781748378","url":"https:\/\/blackandbarhe.com\/products\/the-fibonacci-resonance-and-other-new-golden-ratio-discoveries-maths-music-archaeology-architecture-art-quasicrystals-metamaterials-hardcover","provider":"Black \u0026 Barhe Bookstore","version":"1.0","type":"link"}