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CONTENTS

001 The Art of Problem Solving

005 Key Mathematicians and Mathematical
Texts

019 Arithmetic and Algebra

Problem I: From Luoy¨»n¨À to Ch¨»n¨À¡¯¨»n 021

Problem II: Three Runners 026

Problem III: Nobles and Mandarins 030

Problem IV: Nine Dikes 036

Problem V: Five Canals 040

Problem VI: Rice Tax 042

Problem VII: Pheasants and Hares 046

Problem VIII: Joint Purchase 049

Problem IX: Rectangular Arrays 057

Problem X: Hundred Fowls Problem 067

073 Areas and Volumes

Problem I: Rectangular Field 075

Problem II: Trapezoidal Field 078

Problem III: Circle Field 082

Problem IV: Ring Field 087

Problem V: Pyramid and Cone 093

Problem VI: Sections of A Rectangular Prism 101

Problem VII: Square Frustum 108

Problem VIII: Conical Frustum 112

Problem IX: Mouhefan¨À¨Àai 117

Problem X: Sphere 123

127 Right Triangles

Problem I: Gou¨Àu Diagram 129

Problem II: Winding Vine 133

Problem III: Reed in A Pond 135

Problem IV: The Tall Door 137

Problem V: Broken Bamboo 140

Problem VI: Two Runners 142

Problem VII: Inscribed Square 150

Problem VIII: Inscribed Circle 154

Problem IX: Square Towns 158

Problem X: Sea Island 163

Appendix:Timeline of Chinese
Mathematics 170

References 173


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