5000 years of geometry : mathematics in history and culture / Christoph J. Scriba and Peter Schreiber

Includes bibliographical references and indexes.

Introduction --
1. The beginnings of geometrical representations and calculations --
2. Geometry in the Greek-Hellenistic era and late Antiquity --
3. Oriental and old American geometry --
4. Geometry in the European Middle Ages --
5. New impulses for geometry during the Renaissance --
6. The development of geometry in the 17th and 18th centuries --
7. New paths of geometry in the 19th century --
8. Geometry in the 20th century --
Appendix: Selection of original texts.

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 "Goldon 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 and 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 geometry in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times.