LEADER 03674nam 22006015 450 001 9910965757603321 005 20250731082140.0 010 $a9781461206293 010 $a1461206294 024 7 $a10.1007/978-1-4612-0629-3 035 $a(CKB)3400000000089207 035 $a(SSID)ssj0001296884 035 $a(PQKBManifestationID)11735204 035 $a(PQKBTitleCode)TC0001296884 035 $a(PQKBWorkID)11354236 035 $a(PQKB)10804958 035 $a(DE-He213)978-1-4612-0629-3 035 $a(MiAaPQ)EBC3075040 035 $a(PPN)238006808 035 $a(EXLCZ)993400000000089207 100 $a20121227d1998 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric Constructions /$fby George E. Martin 205 $a1st ed. 1998. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1998. 215 $a1 online resource (XI, 206 p.) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780387982762 311 08$a0387982760 311 08$a9781461268451 311 08$a1461268451 320 $aIncludes bibliographical references and index. 327 $a1 Euclidean Constructions -- 2 The Ruler and Compass -- 3 The Compass and the Mohr-Mascheroni Theorem -- 4 The Ruler -- 5 The Ruler and Dividers -- 6 The Poncelet-Steiner Theorem and Double Rulers -- 7 The Ruler and Rusty Compass -- 8 Sticks -- 9 The Marked Ruler -- 10 Paperfolding -- The Back of the Book -- Suggested Reading and References. 330 $aGeometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations. As specified by Plato, the game is played with a ruler and compass. The first chapter is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never seen. The second chapter formalizes Plato's game and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, using only a compass, using toothpicks, using a ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort. This is as much an algebra book as it is a geometry book. Since all the algebra and all the geometry that are needed is developed within the text, very little mathematical background is required to read this book. This text has been class tested for several semesters with a master's level class for secondary teachers. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aGeometry 606 $aGeometry 615 0$aGeometry. 615 14$aGeometry. 676 $a516 700 $aMartin$b George E$g(George Edward),$f1932-$4aut$4http://id.loc.gov/vocabulary/relators/aut$049095 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910965757603321 996 $aGeometric constructions$9374867 997 $aUNINA