Heavenly Mathematics

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 Mathematics traces 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 elegent proofs and often surprising conclusions. Heavenly Mathematics is 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. -- Jacket.

"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 Mathematics traces 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."--Jacket.

The Mathematics of the Heavens and the Earth is the first major history in English of the origins and early development of trigonometry. Glen Van Brummelen identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and he examines the revolutionary discoveries of Hipparchus, the Greek astronomer believed to have been the first to make systematic use of trigonometry in the second century BC while studying the motions of the stars. The book traces trigonometry's development into a full-fledged mathematical discipline in India and Islam; explores its applications to such areas as geography and seafaring navigation in the European Middle Ages and Renaissance; and shows how trigonometry retained its ancient roots at the same time that it became an important part of the foundation of modern mathematics. The Mathematics of the Heavens and the Earth looks at the controversies as well, including disputes over whether Hipparchus was indeed the father of trigonometry, whether Indian trigonometry is original or derived from the Greeks, and the extent to which Western science is indebted to Islamic trigonometry and astronomy. The book also features extended excerpts of translations of original texts, and detailed yet accessible explanations of the mathematics in them. No other book on trigonometry offers the historical breadth, analytical depth, and coverage of non-Western mathematics that readers will find in The Mathematics of the Heavens and the Earth.

The Almagest is by far the greatest work in astronomy in ancient times. In a massive series of thirteen books, Ptolemy shows how every detail of the motions of the sun, moon, planets, and stars can be expressed using geometrical models that can be used to compute celestial positions with remarkable accuracy The present selection covers all the essential features of Ptolemy s treatment of the heavens, omitting only more difficult and abstruse matters such as the moon s motion and the calculation of eclipses. In the interest of conciseness, development of planetary theories is restricted to two planets, one inferior (Venus) and one superior (Mars). Ptolemy s text is accompanied by extensive notes and introductions that are aimed at making the book accessible to students encountering Ptolemy for the first time. This edition is designed to provide everything needed for a one-semester course, or it can be a component of a more general course on planetary theory or history of astronomy."

A future of designer humans, smart machines, protean technology. Our dwindled descendents exiled to large space stations visit Cleansed Earth occasionally for gravity- and sensory-deprivation therapy. Human longevity, at last attained, ironically creates a Great Plague of Suicidal Despair, Disnovelling, born of the intruding longer prospect of bloody Nature and of the impersonal hurtling cosmic vastitudes. Centwen, a resurrected twentieth century archetype joined by elites and archetypes from other centuries, learns from his tour guides, the superbot, Prodigy, and its human creator, Great Psychodor, about a last-chance project to create not a mythical but a secular, dynamic, intelligent Heaven; and, if it succeeds, whether or not transformed humans and/or their intelligent machines can escape to it.

This book is a history of the development of mathematical astronomy in China, from the late third century BCE, to the early 3rd century CE - a period often referred to as 'early imperial China'. It narrates the changes in ways of understanding the movements of the heavens and the heavenly bodies that took place during those four and a half centuries, and tells the stories of the institutions and individuals involved in those changes. It gives clear explanations of technical practice in observation, instrumentation, and calculation, and the steady accumulation of data over many years - but it centres on the activity of the individual human beings who observed the heavens, recorded what they saw, and made calculations to analyse and eventually make predictions about the motions of the celestial bodies. It is these individuals, their observations, their calculations, and the words they left to us that provide the narrative thread that runs through this work. Throughout the book, the author gives clear translations of original material that allow the reader direct access to what the people in this book said about themselves and what they tried to do.

Poetry. After selling out its British edition, Mandy Kahn's stunning first collection of poems, MATH, HEAVEN, TIME, is now available in an American paperback edition. This is a collection with easy lyricism and clear- eyed wisdom woven effortlessly into its remarkably readable fabric, written by a poet whom World Literature Today calls "a rising star of West Coast poetry," and about whom Flaunt magazine says, "She is that relatively rare cultural anomaly, the professional poet, who confounds the warnings of finger- wagging parents and college counsellors everywhere."

A new partnership of biologists and mathematicians is picking apart the hidden complexity of animals and plants to throw fresh light on the behaviour of entire organisms, how they interact and how changes in biological diversity affect the planet's ecological balance. Mathematics offers new and sometimes startling perspectives on evolution and how patterns of inheritance and population work out over time-scales ranging from millions to hundreds of years - as well as what's going on to change us right now. Ian Stewart, in characteristically clear and entertaining fashion, explores these and a whole range of pertinent issues, including how far genes control behaviour and the nature of life itself. He shows how far mathematicians and biologists are succeeding in tackling some of the most difficult scientific problems the human race has ever confronted and where their research is currently taking us.