This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.
Geometry Civilized is a unique combination of history and mathematics. It contains a full introduction to plane geometry and trigonometry within a fascinating historical framework that sets off the technical material. This approach to geometrical ideas gives the book its unique, readable style. The author has included a wide range of unusual and engaging geometric problems, many of which are taken from practical applications, drawn from sources ranging from ancient to modern. The study of geometry has been an important element of education in Europe since the time of the Greeks. This book helps us to understand why such emphasis has been placed on obtaining a good understanding of geometry. But the history presented here is not confined to the Western tradition. Examples drawn from other cultures, particularly Chinese and Indian, underscore the peculiarities of the geometry we have inherited from the Greeks, and thereby make Euclid's approach more accessible. Book reviews from the hardback: 'He has written a marvellous tale of how, throughout much of recorded history, geometrical thinking and civilisation have been closely intertwined. ...Definitely a book to dip into and reflect on a superior form of brainfood for the beach this summer perhaps? Heilbron's enthusiasm is contagious.' Ian Stewart, New Scientist 'The book is wonderfully illustrated. There are diagrams on almost every page, apt illustrations from older books, and well chosen photographs,together with eight colour plates. The appearance of the book is quite seductive, for which Oxford University Press should be congratulated.' Jeremy Gray, Nature 'This is a handsome book, well researched and entertainingly written. It shows how powerfully a historically informed account can communicate. If you thought Euclidean geometry was something only your great-grandparents did - try it, you will be surprised.' BJune Barrow-Green, The TIMES Higher Education Supplement
Lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet: ob beim Weben oder Flechten einfacher zweidimensionaler Muster oder beim Bauen mit dreidimensionalen Körpern. Das Buch liefert einen faszinierenden Überblick über die geometrischen Vorstellungen und Erkenntnisse der Menschheit von der Urgesellschaft bis hin zu den mathematischen und künstlerischen Ideen des 20. Jahrhunderts.
Basic Approach Developed as a comprehensive introductory work for scholars and students of ancient and early medieval Indian history, this books provides the most exhaustive overview of the subject. Dividing the vast historical expanse from the stone age to the 12th century into broad chronological units, it constructs profiles of various geographical regions of the subcontinent, weaving together and analysing an unparalleled range of literary and archaeological evidence. Dealing with prehistory and protohistory of the subcontinent in considerable detail, the narrative of the historical period breaks away from conventional text-based history writing. Providing a window into the world primary sources, it incorporates a large volume of archaeological data, along with literary, epigraphic, and numismatic evidence. Revealing the ways in which our past is constructed, it explains fundamental concepts, and illuminates contemporary debates, discoveries, and research. Situating prevailing historical debates in their contexts, Ancient and Early Medieval India presents balanced assessments, encouraging readers to independently evaluate theories, evidence, and arguments. Beautifully illustrated with over four hundred photographs, maps, and figures, Ancient and Early Medieval India helps visualize and understand the extraordinarily rich and varied remains of the ancient past of Indian subcontinent. It offers a scholarly and nuanced¿yet lucid¿account of India¿s early past, and will surely transform the discovery of this past into an exciting experience. Tabel of Contents List of photographs List of maps List of figures About the author Preface Acknowledgements A readers guide 1. Understanding Literary and Archaeological Sources 2. Hunter-Gatherers of the Palaeolithic and Mesolithic Ages 3. The Transition to Food Production: Neolithic,Neolithic¿Chalcolithic, and Chalcolithic Villages, c. 7000¿2000 bce 4. The Harappan Civilization, c. 2600¿1900 bce 5. Cultural Transitions: Images from Texts and Archaeology, c. 2000¿600 bce 6. Cities, Kings, and Renunciants: North India, c. 600¿300 bce 7. Power and Piety: The Maurya Empire, c. 324¿187 bce 8. Interaction and Innovation, c. 200 BCE¿300 ce 9. Aesthetics and Empire, c. 300¿600 ce 10. Emerging Regional Configurations, c. 600¿ 1200 ce Note on diacritics Glossary Further readings References Index Author Bio Upinder Singhis Professor in the Department of History at the University of Delhi. She taught history at St. Stephen¿s College, Delhi, from 1981 until 2004, after which she joined the faculty of the Department of History at the University of Delhi. Professor Singh¿s wide range of research interests and expertise include the analysis of ancient and early medieval inscriptions; social and economic history; religious institutions and patronage; history of archaeology; and modern history of ancient monuments. Her research papers have been published in various national and international journals. Her published books include: Kings, Brahmanas, and Temples in Orissa: An Epigraphic Study (AD 300¿1147) (1994); Ancient Delhi (1999; 2nd edn., 2006); a book for children, Mysteries of the Past: Archaeological Sites in India (2002); The Discovery of Ancient India: Early Archaeologists and the Beginnings of Archaeology (2004); and Delhi: Ancient History (edited, 2006).
By establishing a dialogue in which the meditative practices of Buddhism and Christianity speak to the theories of modern philosophy and science, B. Alan Wallace reveals the theoretical similarities underlying these disparate disciplines and their unified approach to making sense of the objective world. Wallace begins by exploring the relationship between Christian and Buddhist meditative practices. He outlines a sequence of meditations the reader can undertake, showing that, though Buddhism and Christianity differ in their belief systems, their methods of cognitive inquiry provide similar insight into the nature and origins of consciousness. From this convergence Wallace then connects the approaches of contemporary cognitive science, quantum mechanics, and the philosophy of the mind. He links Buddhist and Christian views to the provocative philosophical theories of Hilary Putnam, Charles Taylor, and Bas van Fraassen, and he seamlessly incorporates the work of such physicists as Anton Zeilinger, John Wheeler, and Stephen Hawking. Combining a concrete analysis of conceptions of consciousness with a guide to cultivating mindfulness and profound contemplative practice, Wallace takes the scientific and intellectual mapping of the mind in exciting new directions.
The field of geometry reflects a conglomeration of discoveries over time. Filled with detailed diagrams, this insightful volume offers serious students a comprehensive understanding of the fundamentals of geometry, including geometric shapes, axioms, and formulas. In addition, it covers some of the field's most illustrious minds, from Euclid to Wendelin Werner, figures who have helped produce the various branches of geometry as we know them today. This enlightening volume will help students understand the principles of geometry, and also the fascinating story behind the numbers.
Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.
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)
Die Mathematik im mittelalterlichen Islam hatte großen Einfluss auf die allgemeine Entwicklung des Faches. Der Autor beschreibt diese Periode der Geschichte der Mathematik und bezieht sich dabei auf die arabischsprachigen Quellen. Zu den behandelten Themen gehören Dezimalrechnen, Geometrie, ebene und sphärische Trigonometrie, Algebra sowie die Approximation von Wurzeln von Gleichungen. Das Buch wendet sich an Mathematikhistoriker und -studenten, aber auch an alle Interessierten mit Mathematikkenntnissen der weiterführenden Schule.
Profiles ten individuals who have made significant contributions to the field of mathematics, from ancient times to 1300.