LEADER 01976oam 2200481 450 001 9910704177903321 005 20151123082300.0 035 $a(CKB)5470000002437883 035 $a(OCoLC)886560136 035 $a(EXLCZ)995470000002437883 100 $a20140812d1986 ua 0 101 0 $aeng 135 $aurmn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeochemical reconnaissance of late Proterozoic volcanic and mafic plutonic rocks of the Al ?Awshaziyah quadrangle and related rocks in the Qufar quadrangle, Northern Arabian Shield /$fby Gerhard W. Leo 210 1$a[Reston, Va.] :$cDepartment of the Interior, U.S. Geological Survey,$d1986. 210 2$a[Washington, D.C.] :$cUnited States Government Printing Office. 215 $a1 online resource (iii, 16 pages) $cillustrations, maps 225 1 $aU.S. Geological Survey bulletin ;$v1680 300 $aTitle from title screen (viewed Aug. 11, 2014). 320 $aIncludes bibliographical references. 606 $aGeochemistry$zSaudi Arabia$z?Awsaji?yah Region 606 $aGeochemistry$zSaudi Arabia$zQufa?r Region 606 $aGeology, Stratigraphic$yPrecambrian 606 $aVolcanic ash, tuff, etc$zSaudi Arabia$z?Awsaji?yah Region 606 $aVolcanic ash, tuff, etc$zSaudi Arabia$zQufa?r Region 615 0$aGeochemistry 615 0$aGeochemistry 615 0$aGeology, Stratigraphic 615 0$aVolcanic ash, tuff, etc. 615 0$aVolcanic ash, tuff, etc. 700 $aLeo$b Gerhard W.$01388949 712 02$aGeological Survey (U.S.), 801 0$bCOP 801 1$bCOP 801 2$bOCLCO 801 2$bGPO 906 $aBOOK 912 $a9910704177903321 996 $aGeochemical reconnaissance of late Proterozoic volcanic and mafic plutonic rocks of the Al ?Awshaziyah quadrangle and related rocks in the Qufar quadrangle, Northern Arabian Shield$93518958 997 $aUNINA LEADER 03087nam 22005772 450 001 9910790365203321 005 20231102160119.0 010 $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(MiAaPQ)EBC3330416 035 $a(Au-PeEL)EBL3330416 035 $a(CaPaEBR)ebr10729387 035 $a(OCoLC)929120334 035 $a(RPAM)12220236 035 $a(EXLCZ)992670000000205163 100 $a20111104d2000|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe geometry of numbers /$fC.D. Olds, Anneli Lax, Giuliana P. Davidoff$b[electronic resource] 210 1$aWashington :$cMathematical Association of America,$d2000. 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 $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 $aGeometry of numbers 615 0$aGeometry of numbers. 676 $a512/.75 700 $aOlds$b C. D$g(Carl Douglas),$f1912-1979,$01478602 702 $aLax$b Anneli 702 $aDavidoff$b Giuliana P. 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910790365203321 996 $aThe geometry of numbers$93852865 997 $aUNINA