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Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught.Heavenly Mathematicstraces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. 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 for its elegant proofs and often surprising conclusions. Heavenly Mathematicsis illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

The astronomical observations inŚatapatha BrāhamaṇaII.1.2.3 and associated passages in thisBrāhmaṇahave been re-examined to determine what the composers of these passages would have seen in the sky. It is shown that the observation of Kṛttikās described in ŚB II.1.2.3 must have been made before 2250 bce. Examination of othernakṣatrasclose to the celestial equator at 3000 bce shows that the Vedic observers did not mention thesenakṣatrasbecause thesenakṣatraswere far from east and in some cases below the horizon when Kṛttikās were visible at dawn in the east.

The astronomical observations in Śatapatha Brāhamaṇa II.1.2.3 and associated passages in this Brāhmaṇa have been re-examined to determine what the composers of these passages would have seen in the sky. It is shown that the observation of Kṛttikās described in ŚB II.1.2.3 must have been made before 2250 bce. Examination of other nakṣatras close to the celestial equator at 3000 bce shows that the Vedic observers did not mention these nakṣatras because these nakṣatras were far from east and in some cases below the horizon when Kṛttikās were visible at dawn in the east.

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

The Amateur Sky Survey (TASS) is a loose confederation of amateur and professional astronomers. We describe the design and construction of our Mark III system, a set of wide‐field drift‐scan CCD cameras which monitor the celestial equator down to 13th magnitude in several passbands. We explain the methods by which images are gathered, processed, and reduced into lists of stellar positions and magnitudes. Over the period 1996 October to 1998 November, we compiled a large database of photometric measurements. One of our results is thetenxcatcatalog, which contains measurements on the standard Johnson‐Cousins system for 367,241 stars; it contains links to the light curves of these stars as well.