KENNETH R. WILLIAMS., — Triples: Applications of Pythagorean Triples

India Motilal Banarsidass, 2005. 8vo - over 7¾ - 9¾ tall, Hardcover, Hardcover, with dustjacket, New/Dust Jacket Included. ¶ 168P. This book shows an original and highly effective way of unifying many branches of mathematics using Pythagorean triples and Vedic Maths. A simple, elegant method for combining these triples gives unexpected and powerful general methods for solving a wide range of mathematical problems. There are applications in trigonometry (you do not need any of those complicated formulae), coordinate geometry (2 and 3 dimensions), transformations (2 and 3 dimensions), simple harmonic motion, astronomy etc. Contents: 1 TRIPLES: The Triple Theorem; Some Historical Background; Notation for Triples; Equal, Prime and Complementary; Triples; Some Perfect Triples;2 TRIPLE ARITHMETIC; Addition of Triples; Double Angle; Triple Subtraction; Quadrant Angles; Triple Geometry; Angles of 30, 60, 45 etc.; Half Angle; Simplifying Calculations; Summary. 3 TRIPLE TRIGONOMETRY: Introduction; Inverse Functions; The General Triple; Solution of Trigonometrical Equations; Further Trigonometrical Equations- A; Further Trigonometrical Equations- B; Further Trigonometrical Equations- C. 4 TRANSFORMATIONS IN A PLANE: Transposition of the Origin; Rotations; Spirals; Integration of cosx etc.; Rotation of Lines and Curves; Reflections. 5 COORDINATE GEOMETRY: Length of Perpendicular; Foot of Perpendicular; Angle between Two Lines; Equation of a Line; Further Examples. 6 CODE NUMBERS: Grouping Triples; Code Numbers; Geometrical Significance of the Code Numbers; Code Number Pairs; Code Numbers as Triples; Algebraic Formulation; Converting Code Numbers to Triples; Converting Triples to Code Numbers; Addition and Subtraction of Code Numbers; Code Numbers of Code Numbers; Code Numbers of Complementary Triples; Code Numbers of Supplementary Triples; Code Numbers for 0, 90, 180, 270; Relation between Code Numbers and Angles; Further Examples; Summary. 7 SOLUTION OF TRIANGLES: Angle Deficiency Formula; The Sine Formula; The Code Number Formula.8 FURTHER APPLICATIONS OF TRIPLES: Solution of Equations; Complex Numbers; Conics; Difference and Sum of Squares; Incircles and Circumcircles; The Golden Triple; 9 ANGLES IN PERFECT TRIPLES: Revision; Triples and Their Angles; Finding the Angle in a Given Triple; Further Applications of Code Numbers; Finding a Triple with a Given Angle; A Refinement.10 SINE, COSINE, TANGENT & INVERSES: Sine, Cosine and Tangent; Inverse Cosine and Inverse Sine; Inverse Tangent.11 HYPERBOLIC FUNCTIONS: Addition and Subtraction; Double Angle; Equations. 12 APPLIED MATHS APPLICATIONS: Simple Harmonic Motion; Projectiles; Forces in Equilibrium; Work Done by a Force and Moment of a Force. 13 THE TRIPLE METHOD: Range of Application; Deriving the Conventional Formulae; Two Comparisons of the Conventional and Triple Methods. 14 QUADRUPLES: Introduction; Quadruple Generators; Obtaining the Code Numbers of a Perfect Quadruple; The Coordinate Axes; Quadruple Subtraction; Comparative Densities of Perfect Triples and Quadruples. 15 APPLICATIONS OF QUADRUPLES: Coordinate Geometry; Work and Moment; Rotation about Coordinate axis; 3-Dimensional Rotation of Curves; Rotation Conicoids. 16 QUADRUPLES IN ASTRONOMY: Addition of Perpendicular Triples. Change of Coordinate System; Quadruples and Orbits; Quadruple for given i, A; Inclination of Orbit; Quadruple Subtraction;. Quadruple Addition; Doubling and Halving a Quadruple; Code Number Addition and Subtraction; Angle in a Quadruple; Angular Advance; Relationship between d, A; To Obtain a Quadruple with a Given Inclination. PROOFS. ANSWERS TO EXERCISES. REFERENCES. INDEX OF VEDIC FORMULAE. INDEX.