Details for: Van Brummelen G. Heavenly Mathematics.The Forgotten Art..Spheric. Trig. 2013 Rep

Van Brummelen G. Heavenly Mathematics.The Forgotten Art..Spheric. Trig. 2013 Rep

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Textbook in PDF format Mathematical subjects come and go. If you glance at a textbook from a century ago you may recognize some of the contents, but some will be unfamiliar or even baffling. A high school text in analytic geometry, for instance, once contained topics like involutes of circles, hypocycloids, and auxiliary circles of ellipses: topics that most college students today will never see. But spherical trigonometry may be the most spectacular example of changing fashions in the 20th-century mathematics classroom. Born of the need to locate stars and planets in the heavens, for more than 1500 years it was the big brother to the plane trigonometry that high school students slog through today. Navigators on the open seas relied on spherical trigonometry to find their way; lives were lost when their skills failed them. Its dominance continued through the early 20th century: editions of Euclid's Elements that were designed for classrooms often included appendices devoted to this now-forgotten subject. During World War II the popularity of spherical trigonometry remained high. Applications in naval and military settings were touted as motivations, and were given a prominent place in the exercises. Through the early 1950s textbooks continued to be published, although gradually spherical trigonometry found itself relegated to the last major section in a textbook mostly devoted to plane trigonometry. Suddenly, mid-decade, it disappeared, dropped in a pedagogical tide that was heading in other directions. Today almost no trigonometry texts even mention the existence of a spherical counterpart. The only book on the subject continuously in print (Clough-Smith 1966) is difficult to obtain and available only from nautical booksellers. This paucity comes strangely at a time when new applications of spherical trigonometry are being found. GPS devices have some of its formulas built in. It's amusing to see bibliographies of research papers in computer graphics and animation (for use in movies like those made by Pixar) referring to nothing older than last week, except for that stodgy old spherical trig text. So if mathematics teachers have long since given up on spherical trigonometry, why bring it back? The author is not advocating that everyone should dust off the covers of their grandparents' textbooks, but a treasure would be lost if no one did. Heavenly Mathematics How Large Is the Earth? Building a Sine Table with Our Bare Hands The Distance to the Moon Exercises Exploring the Sphere Introducing the Celestial Sphere Spherical Geometry Lunes and Triangles on the Sphere What Is the Smallest and Largest Possible Perimeter ofa Spherical Triangle? Exercises The Ancient Approach Menelaus and His Theorems Abu Sahl al-Kuhi and the Winds of Change Exercises The Medieval Approach Delving Beneath the Surface: Indian Spherical Astronomy Finding the Direction of Mecca Exercises The Modern Approach: Right-Angled Triangles Deriving the Basic Identities Applying the Locality Principle Applying our Knowledge to the Sky and Sea Napier and the Birth of Logarithms Symmetries Codified: The "Pentagramma mirificum" Exercises The Modern Approach: Oblique Triangles Using the Law of Cosines Delambre's and Napier's Analogies Exercises Areas, Angles, and Polyhedra Euler's Polyhedral Formula The Regular Polyhedra Exercises Stereographic Projection Using Stereographic Projection to Solve Triangles A Crystallographic Breakthrough: The Cesaro Method Exercises Navigating by the Stars Preparing to Navigate: The Observations A Digression: The Haversine The Method of Saint Hilaire Exercises Where to Go from Here Appendix Ptolemy's Determination of the Sun's Position Textbooks Further Reading Index

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1. Van Brummelen G. Heavenly Mathematics.The Forgotten Art..Spheric. Trig. 2013.pdf3.56 MiB