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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.