{"product_id":"upon-this-mountain-book-mary-elizabeth-mccormack-9780947916091","title":"Upon This Mountain","description":"This unique book overturns our ideas about non-Euclidean geometry and explains the role of the golden ratio in Euclid's Elements. It highlights a new view on Euclid's Elements and the history of mathematics based on Proclus' hypothesis. It describes a general theory of recursive hyperbolic functions based on the golden, silver, and other metallic proportions. The book contains an original solution of Hilbert's Fourth Problem for hyperbolic and spherical geometries, and puts forward a problem searching for new hyperbolic and spherical worlds of nature based on this solution. For the first time, the book describes the golden qualitative theory of dynamical systems based on the mathematics of harmony. It is intended for a wide range of readers, who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems and dynamical systems.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49569830895889,"sku":"GOR003571992","price":21.99,"currency_code":"USD","in_stock":false},{"title":"GB \/ LIKE_NEW \/ INTERNAL","offer_id":52394315317521,"sku":"GOR011434797","price":13.39,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0947916091.jpg?v=1751364097","url":"https:\/\/www.worldofbooks.com\/products\/upon-this-mountain-book-mary-elizabeth-mccormack-9780947916091","provider":"World of Books ","version":"1.0","type":"link"}