This book is generously illustrated with diagrams from medieval manuscripts of Geminos's text, as well as drawings and photographs of ancient astronomical instruments. It will be of great interest to students of the history of science, to classicists, and to professional and amateur astronomers who seek to learn more about the origins of their science."

Ptolemy's Geography is the only book on cartography to have survived from the classical period and one of the most influential scientific works of all time. Written in the second century AD, for more than fifteen centuries it was the most detailed topography of Europe and Asia available and the best reference on how to gather data and draw maps. Ptolemy championed the use of astronomical observation and applied mathematics in determining geographical locations. But more importantly, he introduced the practice of writing down coordinates of latitude and longitude for every feature drawn on a world map, so that someone else possessing only the text of the Geography could reproduce Ptolemy's map at any time, in whole or in part, at any scale. Here Berggren and Jones render an exemplary translation of the Geography and provide a thorough introduction, which treats the historical and technical background of Ptolemy's work, the contents of the Geography, and the later history of the work.

This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.

This book presents an account of selected topics from key mathematical works of medieval Islam, based on the Arabic texts themselves. Many of these works had a great influence on mathematics in Western Europe. Topics covered in the first edition include arithmetic, algebra, geometry, trigonometry, and numerical approximation; this second edition adds number theory and combinatorics. Additionally, the author has included selections from the western regions of medieval Islam—both North Africa and Spain. The author puts the works into their historical context and includes numerous examples of how mathematics interacted with Islamic society.

The shamanic flight of ecstasy distinguishes shamanism from other spiritual and healing practices. By healing themselves of dysfunctional, outworn, or egocentric patterns and beliefs, shamans provide the model for the greater community to heal and transform itself. Integration of the ecstatic experience into modern culture is crucial to humanity's continued survival and unfolding destiny as partner with the earth.

This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein include selections from the mathematical and computational literature over four millennia, a variety of historical studies on the cultural significance of the number, and an assortment of anecdotal, fanciful, and simply amusing pieces. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, new translations of works by Viete and Huygen, as well as Kaplansky's never-before-published "Song of Pi." From the reviews of earlier editions: "Few mathematics books serve a wider potential readership than does a source book and this particular one is admirably designed to cater for a broad spectrum of tastes: professional mathematicians with research interest in related subjects, historians of mathematics, teachers at all levels searching out material for individual talks and student projects, and amateurs who will find much to amuse and inform them in this leafy tome. The authors are to be congratulated on their good taste in preparing such a rich and varied banquet with which to celebrate pi." - Roger Webster for the Bulletin of the LMS "The judicious representative selection makes this a useful addition to one's library as a reference book, an enjoyable survey of developments and a source of elegant and deep mathematics of different eras." - Ed Barbeau for MathSciNet "Full of useful formulas and ideas, it is a vast source of inspiration to any mathematician, A level and upwards-a necessity in any maths library." - New Scientist

Originally published in 1996, this book contains a translation and study of Euclid's Phaenomena, a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid's geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of Ptolemy's Almagest. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with Euclid's Optics one has the beginnings of the history of science as an application of mathematics.

Shadows loom from a forbidden continent. Secret lineages are at last revealed. And time is running out. On Earth, Maeve is able to wield magics unlike anything before. Minds open to her, and blue fire races between her fingers. Her heart aches to return to the Realms, and Rodan, even though the trials await. Yet to do so would guarantee future pain. In Visantium, Rodan is confronted by the sorcerer king Sebastian, and learns that there are more traps awaiting him on the road to the final duel. No matter how prepared he is, he cannot claim victory unless he first accomplishes a cutting personal challenge involving Maeve. Worlds apart, the pair must reunite in order to overcome the growing threat from Attica, and to ensure their joined destiny. The sequel to Catching Pathways, Catching Embers is the next book in the ongoing Five Realms series. Content Warning:Catching Embers is an adult dark fantasy romance, with events both past and present which could be triggering. Read with care.

There is no such thing as safe. Time is the plaything of the gods. Though the trials are over, the duel concluded, Maeve and Rodan face some of their most intense challenges to date in Catching Shadows, the finale to the Five Realms series. Maeve is imprisoned on Attica, at the mercy of the Nyx horde. Rodan is the only force upon the Realms who could stand a chance of saving her, but he has disappeared. Jen, Troy, and Pike are faced with the challenge of how to aid them both. Meanwhile, on Earth, there are stirrings of a great power. One that has the potential to topple not just one world, but all those connected to it. And one that has the ability to strike to the core of Maeve, Rodan, and all they hold close. A sweeping finale touching upon multiple worlds and their ultimate fates. Content Warning: Catching Shadows is an adult dark fantasy romance, with events both past and present which could be triggering. Read with care.

In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors—Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)—are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.