LEADER 03177nam 2200625Ia 450 001 9910966748003321 005 20200520144314.0 010 $a0-88385-955-6 035 $a(CKB)2670000000205163 035 $a(EBL)3330416 035 $a(OCoLC)923220108 035 $a(SSID)ssj0000577632 035 $a(PQKBManifestationID)11376743 035 $a(PQKBTitleCode)TC0000577632 035 $a(PQKBWorkID)10562363 035 $a(PQKB)11199582 035 $a(UkCbUP)CR9780883859551 035 $a(Au-PeEL)EBL3330416 035 $a(CaPaEBR)ebr10729387 035 $a(OCoLC)929120334 035 $a(RPAM)12220236 035 $a(MiAaPQ)EBC3330416 035 $a(EXLCZ)992670000000205163 100 $a20001102d2000 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe geometry of numbers /$fC.D. Olds, Anneli Lax, Giuliana P. Davidoff 205 $a1st ed. 210 $aWashington, DC $cMathematical Association of America$dc2000 215 $a1 online resource (xvi, 174 pages) $cdigital, PDF file(s) 225 1 $aThe Anneli Lax new mathematical library ;$vv. 41 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 08$a0-88385-643-3 320 $aIncludes bibliographical references and index. 327 $aLattice Points and Number Theory -- An Introduction to the Geometry of Numbers -- Gaussian Integers, by Peter D. Lax -- The Closest Packing of Convex Bodies -- Brief Biographies -- Solutions and Hints. 330 $aThe Geometry of Numbers presents a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice-points on lines, circles, and inside simple polygons in the plane. Little mathematical expertise is required beyond an acquaintance with those objects and with some basic results in geometry. The reader moves gradually to theorems of Minkowski and others who succeeded him. On the way, he or she will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres. An appendix by Peter Lax gives a lovely geometric proof of the fact that the Gaussian integers form a Euclidean domain, characterizing the Gaussian primes, and proving that unique factorization holds there. In the process, he provides yet another glimpse into the power of a geometric approach to number theoretic problems. 410 0$aAnneli Lax new mathematical library ;$vv. 41. 606 $aGeometry of numbers 606 $aNumber theory 615 0$aGeometry of numbers. 615 0$aNumber theory. 676 $a512/.75 700 $aOlds$b C. D$g(Carl Douglas),$f1912-$040856 701 $aLax$b Anneli$042255 701 $aDavidoff$b Giuliana P$0622037 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910966748003321 996 $aThe geometry of numbers$94403610 997 $aUNINA