{"product_id":"the-geometry-of-numbers-paperback","title":"The Geometry of Numbers - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eC. D. Olds\u003c\/b\u003e (Author), \u003cb\u003eAnneli Lax\u003c\/b\u003e (Author), \u003cb\u003eGiuliana P. Davidoff\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThis is a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice points on lines, circles and inside simple polygons in the plane. A minimum of mathematical expertise is required beyond an acquaintance with elementary geometry. The authors gradually lead up to the theorems of Minkowski and others who succeeded him. On the way the reader will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 192\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 22, 2001\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337182626041,"sku":"9780883856437","price":50.47,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/9qHLnUsF1L9780883856437.webp?v=1769675443","url":"https:\/\/bookscloud.io\/products\/the-geometry-of-numbers-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}