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.

"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 Heavens on Earth explores the place of the observatory in nineteenth-century science and culture. Astronomy was a core pursuit for observatories, but usually not the only one. It belonged to a larger group of “observatory sciences” that also included geodesy, meteorology, geomagnetism, and even parts of physics and statistics. These pursuits coexisted in the nineteenth-century observatory; this collection surveys them as a coherent whole. Broadening the focus beyond the solitary astronomer at his telescope, it illuminates the observatory’s importance to technological, military, political, and colonial undertakings, as well as in advancing and popularizing the mathematical, physical, and cosmological sciences. The contributors examine “observatory techniques” developed and used not only in connection with observatories but also by instrument makers in their workshops, navy officers on ships, civil engineers in the field, and many others. These techniques included the calibration and coordination of precision instruments for making observations and taking measurements; methods of data acquisition and tabulation; and the production of maps, drawings, and photographs, as well as numerical, textual, and visual representations of the heavens and the earth. They also encompassed the social management of personnel within observatories, the coordination of international scientific collaborations, and interactions with dignitaries and the public. The state observatory occupied a particularly privileged place in the life of the city. With their imposing architecture and ancient traditions, state observatories served representative purposes for their patrons, whether as symbols of a monarch’s enlightened power, a nation’s industrial and scientific excellence, or republican progressive values. Focusing on observatory techniques in settings from Berlin, London, Paris, and Rome to Australia, Russia, Thailand, and the United States, The Heavens on Earth is a major contribution to the history of science. Contributors: David Aubin, Charlotte Bigg, Guy Boistel, Theresa Levitt, Massimo Mazzotti, Ole Molvig, Simon Schaffer, Martina Schiavon , H. Otto Sibum, Richard Staley, John Tresch, Simon Werrett, Sven Widmalm

Numbers surround us. Just try to make it through a day without using any. It's impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. For instance: What timely invention was tampered with by the Caesars and almost perfected by a pope? Why did ten days vanish in September of 1752? How did Queen Victoria shorten the Sunday sermons at chapel? What important invention caused the world to be divided into time zones? What simple math problem caused the Mars Climate Orbiter to burn up in the Martian atmosphere? What common unit of measurement was originally based on the distance from the equator to the North Pole? Does water always boil at 212? Fahrenheit? What do Da Vinci's Last Supper and the Parthenon have in common? Why is a computer glitch called a "bug"? It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.

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."

Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell.

"Simple, clear explanations of twenty ways in which mathematics helps us to understand practical issues of everyday life. Suitable for teenagers and adults, and beautifully produced. Highly recommended!" - Professor Ian Stewart, bestselling author of The Cabinet of Mathematical Curiosities Mathematics is an indispensable tool for life. From the systems that underpin our newsfeeds, through to the data analysis that informs our health and financial decisions, to the algorithms that power how we search online – mathematics is at the heart of how our modern world functions. In 20 dip-in lessons, Understanding Numbers explains how and why mathematics fuels your world and arms you with the knowledge to make wiser choices in all areas of your life. • Make sense of health statistics • Understand the mathematics behind political voting systems • Get to grips with how online search tools work • Discover how mathematics can create the perfect city