Marvels of Math. Fascinating Reads and Awesome Activities. Kendall Haven
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1 Marvels of Math Fascinating Reads and Awesome Activities Kendall Haven 1998 Teacher Ideas Press A Division of Libraries Unlimited, Inc. Englewood, Colorado
2 Contents INTRODUCTION ix Stories About Numbers Numbers in the Sand The Invention of Irrational Numbers by the Pythagoreans circa 520 BC 3 At a Glance 3 Terms to Know 3 Numbers in the Sand 5 Follow-on Questions and Activities to Explore 12 Something from Nothing The Invention of Zero as a Number by al-khwarizmi in AD At a Glance 13 Terms to Know 14 Something from Nothing, 15 Follow-on Questions and Activities to Explore 22 Imagine That... The Invention of Imaginary Numbers by Rafael Bombelli in At a Glance 23 Terms to Know 24 Imagine That 25 Follow-on Questions and Activities to Explore 30
3 vi Contents Infinity... and Beyond! The Invention of "Surreal" Numbers by John Conway and Martin Kruskal in At a Glance ;. 31 Terms to Know 32 Infinity... and Beyond! 33 Follow-on Questions and Activities to Explore 39 Stories About Geometry Elementary Elements The Invention of Euclidean Geometry by Euclid in 295 BC 43 At a Glance 43 Terms to Know 44 Elementary Elements 45 Follow-on Questions and Activities to Explore 50 "Flying" High The Invention oj Cartesian Coordinates by Rene Descartes in the 1620s At a Glance 51 Terms to Know 51 'Flying"High 53 Follow-on Questions and Activities to Explore 59 Shadow Boxing The Invention of Perspective Geometry by Girard Desargues in 1635 ; At a Glance 60 Terms to Know 60 Shadow Boxing 62 Follow-on Questions and Activities to Explore 69 Stories About Mathematical Concepts The Weighing Game The Invention of Specific Gravity and Buoyancy by Archimedes in 232 BC.. 73 At a Glance 73 Terms to Know 73 The Weighing Game 75 Follow-on Questions and Activities to Explore 81
4 Contents vii The Odds Are... The Invention of Probability Theory by Pierre de Fermat in At a Glance 83 Terms to Know 83 The Odds Are 85 Follow-on Questions and Activities to Explore 92 Smaller Makes Bigger The Invention of Calculus by Isaac Newton in At a Glance 93 Terms to Know 94 Smaller Makes Bigger 95 Follow-on Question and Activity to Explore 102 A Bridge to Math The Invention of Topology by Leonhard Euler in At a Glance 104 Terms to Know 104 A Bridge to Math 106 Follow-on Questions and Activities to Explore 112 The Truth About "M. Le Blanc" Sophie Germain's Start Toward Her Development of the Theory of Elasticity in At a Glance, Terms to Know 113 The Truth About "M.Le Blanc" 114 Follow-on Questions and Activities to Explore 119 Out of Time The Invention of Group Theory by Evarstie Galois in At a Glance 120 Terms to Know 120 Out of Time 122 Follow-on Questions and Activities to Explore 128
5 viii Contents One Step Forward, One Step Back The Theory of Sequences and Improved Algebraic Solutions by Sonya Kovalevsky in the 1870s 129 At a Glance 129 Terms to Know 129 One Step Forward, One Step Back 131 Follow-on Questions and Activities to Explore 138 Stories About Calculating Machines No Bones About It! The Invention of "Napier's Bones" by John Napier in At a Glance 141 Terms to Know 141 No Bones About It! 143 Follow-on Questions and Activities to Explore 150 Amazing Grace The Invention of Computer Languages by Grace Hopper in At a Glance 152 Terms to Know 153 Amazing Grace 154 Follow-on Questions and Activities to Explore 159 REFERENCES V. 161 INDEX 167 ABOUT THE AUTHOR 172
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