"Practical, scientific, philosophical & artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these-the search for beauty. Mathematics is an art, & as such affords the pleasures which all the arts afford."--The Author Preface Why mathematics? A historical orientation Logic & mathematics Number: the fundamental concept Algebra, the higher arithmetic The nature & uses of Euclidean geometry Charting the earth & the heavens The mathematical order of nature The awakening of Europe Mathematics & painting in the Renaissance Projective geometry Coordinate geometry The simplest formulas in action Parametric equations & curvilinear motion The application of formulas to gravitation The differential calculus The integral calculus Trigonometric functions & oscillatory motion The trigonometric analysis of musical sounds Non-Euclidean geometries & their significance Arithmetics & their algebras The statistical approach to the social & biological sciences The theory of probability The nature & values of mathematics Table of Trigonometic Ratios Answers to Selected & Review Exercises Additional Answers & Solutions Index
"Practical, scientific, philosophical & artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these-the search for beauty. Mathematics is an art, & as such affords the pleasures which all the arts afford."--The Author Preface Why mathematics? A historical orientation Logic & mathematics Number: the fundamental concept Algebra, the higher arithmetic The nature & uses of Euclidean geometry Charting the earth & the heavens The mathematical order of nature The awakening of Europe Mathematics & painting in the Renaissance Projective geometry Coordinate geometry The simplest formulas in action Parametric equations & curvilinear motion The application of formulas to gravitation The differential calculus The integral calculus Trigonometric functions & oscillatory motion The trigonometric analysis of musical sounds Non-Euclidean geometries & their significance Arithmetics & their algebras The statistical approach to the social & biological sciences The theory of probability The nature & values of mathematics Table of Trigonometic Ratios Answers to Selected & Review Exercises Additional Answers & Solutions Index