{"product_id":"pi-and-phi-james-r-warren-9781915750068","title":"Pi and Phi: A Coy Romance of Two Numbers","description":"In this selective conspectus mathematician and essayist James Warren takes an in-depth look at the Ludolphine Constant, p, and its relationships ( if any ) with the Phidian Ratio, F, sometimes called the Golden Section. Simply-defined and deeply-mysterious the two numbers' many go-betweens include algebraic, trigonometric and hyperbolic functions and yet there is no simple finite equation relating them, though many such structures come very close! The quality of estimators is part of the underlying science of this intricate liaison. Both numbers share the protean interpretabilities of great art and literature, and yet also seem to reflect the realities of growth in the physical and biological worlds. If you read this book and then understand the relationship entirely, then I have not done my job. This corrected and extended Second Edition continues the examination of the Pi-Phi relationship until 2023.\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e James R. Warren\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1915750067\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781915750068\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Midland Tutorial Productions\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/01\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 426\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.67lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.00h x 7.00w x 1.31d","brand":"James R. Warren","offers":[{"title":"Hardcover","offer_id":44652243615999,"sku":"9781915750068","price":75.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_e0dc0704-74f0-4ade-8223-0e6ce48c22a9.jpg?v=1704215226","url":"https:\/\/www.whiterainbookhouse.com\/products\/pi-and-phi-james-r-warren-9781915750068","provider":"WR Book House","version":"1.0","type":"link"}