LEADER 02851nam 2200553Ia 450 001 9910971363803321 005 20200520144314.0 010 $a0-88385-922-X 035 $a(CKB)2560000000081416 035 $a(SSID)ssj0000667039 035 $a(PQKBManifestationID)11378768 035 $a(PQKBTitleCode)TC0000667039 035 $a(PQKBWorkID)10673764 035 $a(PQKB)10713492 035 $a(UkCbUP)CR9780883859223 035 $a(MiAaPQ)EBC3330385 035 $a(Au-PeEL)EBL3330385 035 $a(CaPaEBR)ebr10729356 035 $a(OCoLC)929120472 035 $a(RPAM)1694420 035 $a(EXLCZ)992560000000081416 100 $a20111006d1961 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric inequalities /$fby Nicholas D. Kazarinoff 205 $a1st ed. 210 $aWashington, DC $cMathematical Association of America$d1961 215 $a1 online resource (132 pages) $cdigital, PDF file(s) 225 0 $aAnneli Lax New Mathematical Library ;$vno. 4 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 08$a0-88385-604-2 327 $aFront Cover -- Geometric Inequalities -- Copyright Page -- CONTENTS -- Preface -- Chapter 1. Arithmetic and Geometric Means -- 1.1 Fundamentals -- 1.2 The Theorem of Arithmetic and Geometric Means -- Chapter 2. Isoperimetric Theorems -- 2.1 Maxima and minima -- 2.2 Isoperimetric theorems for triangles -- 2.3 Isoperimetric theorems for polygons -- 2.4 Steiner's attempt -- Chapter 3. The Reflection Principle -- 3.1 Symmetry -- 3.2 Dido's problem -- 3.3 Steiner symmetrization -- 3.4 Conic sections -- 3.5 Triangles -- Chapter 4. Hints and Solutions -- Index of Numhered Theorems -- Back Cover. 330 $aAnybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students. 606 $aGeometry, Plane 606 $aInequalities (Mathematics) 615 0$aGeometry, Plane. 615 0$aInequalities (Mathematics) 676 $a513.1 700 $aKazarinoff$b Nicholas D$041085 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971363803321 996 $aGeometric inequalities$981658 997 $aUNINA