TRIPLES: Applications Of Pythagorean Triples

Hardcover; New; 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 0Â, 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.