A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)

In The Spatial Reformation, Michael J. Sauter offers a sweeping history of the way Europeans conceived of three-dimensional space, including the relationship between Earth and the heavens, between 1350 and 1850. He argues that this "spatial reformation" provoked a reorganization of knowledge in the West that was arguably as important as the religious Reformation. Notably, it had its own sacred text, which proved as central and was as ubiquitously embraced: Euclid's Elements. Aside from the Bible, no other work was so frequently reproduced in the early modern era. According to Sauter, its penetration and suffusion throughout European thought and experience call for a deliberate reconsideration not only of what constitutes the intellectual foundation of the early modern era but also of its temporal range. The Spatial Reformation contends that space is a human construct: that is, it is a concept that arises from the human imagination and gets expressed physically in texts and material objects. Sauter begins his examination by demonstrating how Euclidean geometry, when it was applied fully to the cosmos, estranged God from man, enabling the breakthrough to heliocentrism and, by extension, the discovery of the New World. Subsequent chapters provide detailed analyses of the construction of celestial and terrestrial globes, Albrecht Dürer's engraving Melencolia, the secularization of the natural history of the earth and man, and Hobbes's rejection of Euclid's sense of space and its effect on his political theory. Sauter's exploration culminates in the formation of a new anthropology in the eighteenth century that situated humanity in reference to spaces and places that human eyes had not actually seen. The Spatial Reformation illustrates how these disparate advancements can be viewed as resulting expressly from early modernity's embrace of Euclidean geometry.

Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

Places of Encounter provides a place-based approach to world history, focusing on specific locations at critical moments when human history was transformed as a result of encounters-physical, political, cultural, intellectual, and religious. Original, contributed essays by leading academics in the field explore places from Hadar to Xi'an, Salvador to New York, and numerous other locations that have produced historical shockwaves and significant global impact throughout history. With a chronologically organized table of contents, each chapter dissects a particular moment in history, with personal commentary from each contributor, a narrative of the location's historical significance at the time, and a section on significant global connections. Primary sources and discussion questions at the end of each chapter allow students a view into the lives of individuals of the time. Students will experience the narrative of historic individuals as well as modern scholars looking back over documentation to offer their own views of the past, providing students with the perfect opportunity to see how scholars form their own views about history.

Work in Progress offers the first in-depth study of the cultural and social importance of literary revision among ancient Greek and Roman authors.

In Proclus' penetrating exposition of Euclid's methods and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strength of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere. This is virtually the only work surviving from antiquity that deals with what we today would call the philosophy of mathematics.