Triples: Applications of Pythagorean Triples (India Scientific Heritage) by Kenneth Williams (2003) Hardcover

Pythagorean triples, like 3, 4, 5 have been a fascination for thousands of years. Now for the first time a simple elegant system, based on these triples, has been developed which reveals unexpected applications in many areas of pure and applied mathematics. These include general applications in trigonometry, coordinate geometry (in 2 and 3 dimensions), transformations (in 2 and 3 dimensions), simple harmonic motion, astronomy etc. The easy triple method links these areas and replaces large numbers of apparently unconnected formulae with a single device. This book fully explains the various applications and most of it should be accessible to anyone with the basic understanding of mathematics which a school leaver should have. Cover 1 About Triples 2 Title page 4 © 2009 6 Dedication 6 PREFACE 8 FOREWORD 10 CONTENTS 12 1 - TRIPLES 16 2 - TRIPLE ARITHMETIC' 22 3 - TRIPLE TRIGONOMETRY 34 4 - TRANSFORMATIONS IN A PLANE 48 5 - COORDINATE GEOMETRY 60 6 - TRIPLE CODE NUMBERS 66 7 - SOLUTION OF TRIANGLES 82 8 - FURTHER APPLICATIONS OF TRIPLES 90 9 - ANGLES IN PERFECT TRIPLES 102 10 - SINE, COSINE, TANGENT AND INVERSES 114 11 - HYPERBOLIC FUNCTIONS 122 12 - APPLIED MATHEMATICS APPLICATIONS 128 13 - THE TRIPLE METHOD 140 14 - QUADRUPLES 146 15 - APPLICATIONS OF QUADRUPLES 151 16 - QUADRUPLES IN ASTRONOMY 160 APPENDIX: Proofs etc. 174 ANSWERS 180 REFERENCES 182 INDEX OF VEDIC FORMULAE 184 INDEX 184 About the Author 189 Back Cover 190 scanned,to,PDF,by,gnv64 scanned to PDF by gnv64 Pythagorean triples like 3,4,5 have been a fascination for thousands of years. Now for the first time a simple elegant system, based on these triples, has been developed which reveals unexpected applications in many areas of pure and applied mathematics.These include general applications is trigonometry, coordinate geometry (in 2 and 3 dimensions), transformations (in 2 and 3 dimensions), simple harmonic motions, projectile motion, astronomy etc.The easy triple method links these areas and replaces large numbers of apparently unconnected formulae with a single device.This book fully explains the various applications and most of it should be accessible to anyone with the basic understanding of mathematics which a school leaver should have.