{"product_id":"the-cube-a-window-to-convex-and-discrete-geometry-hardback-9780521855358","title":"The Cube-A Window to Convex and Discrete Geometry (Hardback) 9780521855358","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Cube-A Window to Convex and Discrete Geometry\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAnalysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eChuanming Zong (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521855358, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 2 February 2006\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e184 pages, 6 b\/w illus.\u003cbr\u003e23.5 x 15.2 x 1.5 cm, 0.394 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended.\" -- Choice\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0\/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Basic notation\u003cbr\u003e 0. Introduction\u003cbr\u003e 1. Cross sections\u003cbr\u003e 2. Projections\u003cbr\u003e 3. Inscribed simplices\u003cbr\u003e 4. Triangulations\u003cbr\u003e 5. 0\/1 polytopes\u003cbr\u003e 6. Minkowski's conjecture\u003cbr\u003e 7. Furtwangler's conjecture\u003cbr\u003e 8. Keller's conjecture\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Topology [\u003ca title=\"See our other books on Topology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Topology%20%5BPBP%5D%22\"\u003ePBP\u003c\/a\u003e], Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006026109208,"sku":"9780521855358","price":112.97,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521855358i_7501ce85-48ee-4c3c-983a-81b547b094cc.jpg?v=1691358399","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-cube-a-window-to-convex-and-discrete-geometry-hardback-9780521855358","provider":"Freshly Printed Books","version":"1.0","type":"link"}