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. Nadenik (Czech Technical University in Prague)

Writing the History of Mathematics provides both an intellectual and a social history of the development of the subject from the first such effort written in ancient Greece to recent efforts in the 20th century. A special project of the International Commission on History of Mathematics, this work is the result of more than ten years of collaboration by a team of 32 experts, each writing about the history of mathematics in their own countries or regions, and drawing upon extensive research and archival study. In addition to individuals, such institutions as universities, academies, institutes, libraries, and the like are also covered, including journals, encyclopedias, and other collective projects that promote history of mathematics. The book also includes portraits of twenty-five historians of mathematics.

Schon lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet. So entstehen beim Weben und Flechten einfache zweidimensionale Muster und ohne dreidimensionale Korper wie Quader, Wurfel oder Pyramide ist keine Bautatigkeit denkbar. Das vorliegende Buch gibt einen faszinierenden Uberblick uber die geometrischen Vorstellungen und Erkenntnisse der Menschen von der Urgesellschaft bis hin zu den komplexen mathematischen wie auch kunstlerischen Ideen des 20. Jahrhunderts. Neben vielen Abbildungen wird jede Epoche mit einer Tabelle zeit- und kulturgeschichtlicher Daten eingeleitet und mit einer tabellarischen Darstellung der wesentlichen Inhalte der Geometrie dieser Zeit abgeschlossen. Aufgaben am Ende jeden Kapitels laden den Leser ein, sich an den Problemen der alten Meister selber zu versuchen. Ein Buch fur alle, die der Lebendigkeit und Entwicklung der Geometrie als erste "Anwendungswissenschaft" nachspuren wollen.

Fur die 3. Auflage wurden neuste Forschungsergebnisse uber steinzeitliche Kreisgrabenanlagen und die Himmelsscheibe von Nebra aus der Bronzezeit aufgenommen. Zahlreiche Abbildungen, viele davon jetzt in Farbe, erhohen den Lesegenuss des Buches."

The Correspondence of John Wallis (1616 -1703) is a critically acclaimed resource in the history of early modern science. Volume IV covers the period from 1672 to April 1675 and contains over eighty previously unpublished letters. It documents Wallis's role in the crucial debate over the method of tangents involving figures such as Sluse, James Gregory, Hudde, Barrow, Newton, and Christiaan Huygens. In this way it illuminates further an important part of the history of the calculus. Wallis's letters also provide valuable new insights into mathematical book production and the importance of the international exchange of books in the growth and dissemination of mathematical knowledge. We learn more about the part played by the intelligencer John Collins and the astronomer royal John Flamsteed in the edition of Jeremiah Horrox's Opera posthuma, published by Wallis in 1673. There are also new insights on the background to Wallis's early work on equations, and the reasons why he criticized Gaston Pardies's proposed tract on motion. The causes of the breakdown in Wallis's epistolary relation to Christiaan Huygens following the publication of the Horologium oscillatorium in 1673 are also revealed. Many letters reflect Wallis's active involvement in the Royal Society. Through the medium of correspondence the Savilian professor participated in numerous debates such as those over the anomalous suspension of mercury in the Torricellian tube or Hevelius's use of plain sights in positional astronomy. The volume allows us to gain a deeper understanding of the background to these debates. Furthermore, the volume throws important new light on the history of the University of Oxford and of the University Press in the early modern period. As keeper of the University Archives, Wallis was one of the institution's highest officers. Scarcely any event of note concerning the University did not require his involvement in some way, and this is reflected in numerous letters and documents which the volume publishes for the first time.