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The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler’s proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.
Mathematics --- Mathematical recreations. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Arbitrarily large. --- Arithmetic. --- Big O notation. --- Binomial theorem. --- Bonse's inequality. --- Circumference. --- Coefficient. --- Combination. --- Complete theory. --- Computation. --- Coprime integers. --- Diameter. --- Divisor. --- Equilateral triangle. --- Euler's formula. --- Euler's theorem. --- Exterior (topology). --- Factorial. --- Factorization. --- Fermat's Last Theorem. --- Fermat's theorem. --- Fourth power. --- Fractional part. --- Geometric mean. --- Geometric series. --- Geometry. --- Hypotenuse. --- Integer factorization. --- Intersection (set theory). --- Irrational number. --- Line segment. --- Logarithm. --- Long division. --- Mathematical induction. --- Mathematics. --- Metric space. --- Natural number. --- Non-Euclidean geometry. --- Number theory. --- Parallelogram. --- Parity (mathematics). --- Pedal triangle. --- Perfect number. --- Polyhedron. --- Power of 10. --- Prime factor. --- Prime number theorem. --- Prime number. --- Prime power. --- Pure mathematics. --- Pythagorean theorem. --- Rational number. --- Rectangle. --- Regular polygon. --- Regular polyhedron. --- Remainder. --- Reuleaux triangle. --- Rhomboid. --- Rhombus. --- Right angle. --- Right triangle. --- Scientific notation. --- Sign (mathematics). --- Special case. --- Straightedge. --- Summation. --- Theorem. --- Transfinite number. --- Variable (mathematics). --- Waring's problem.
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Heavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950's. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Spherical trigonometry. --- Trigonometry. --- Trig (Trigonometry) --- Geometry --- Mathematics --- Trigonometry, Spherical --- Trigonometry --- Abū 'l-Wafā. --- Abū Mahmūd al-Khujandī. --- Abū Nasr Mansūr ibn 'Alī ibn 'Irāq. --- Abū Sahl al-Kūhī. --- Albert Girard. --- B. M. Brown. --- Cesàro method. --- Christopher Columbus. --- Claudius Ptolemy. --- Earth. --- Elements. --- Georg Rheticus. --- Giuseppe Cesàro. --- Hipparchus of Rhodes. --- Islam. --- Islamic religious rituals. --- John Harrison. --- John Napier. --- Law of Cosines. --- Law of Sines. --- Leonhard Euler. --- Mathematical Collection. --- Mecca. --- Menelaus of Alexandria. --- Menelaus's Theorem. --- Moon. --- Napier's Rules. --- Opus palatinum. --- Planisphere. --- Ptolemy. --- Pythagorean Theorem. --- Rule of Four Quantities. --- Sphaerica. --- Sun. --- acute-angled triangle. --- angle. --- area. --- astrolabe. --- astronomical triangle. --- astronomy. --- cartography. --- celestial motion. --- celestial sphere. --- chronometer. --- classical Greece. --- dead reckoning. --- ecliptic. --- equatorial coordinates. --- geography. --- locality principle. --- logarithms. --- marteloio. --- mathematics. --- method of Saint Hilaire. --- navigation. --- oblique triangle. --- pentagramma mirificum. --- planar Law of Sines. --- plane trigonometry. --- planets. --- polygon. --- polyhedron. --- qibla. --- regular polyhedron. --- right-angled triangle. --- rising time. --- sphere. --- spherical Law of Sines. --- spherical astronomy. --- spherical geometry. --- spherical triangle. --- spherical trigonometry. --- star. --- stars. --- stereographic projection. --- table of sine. --- theorems. --- triangle. --- trigonometric table. --- trigonometry.
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