5000 Years of Geometry

Mathematics in History and Culture

Author: Christoph J. Scriba,Peter Schreiber

Publisher: Birkhäuser

ISBN: 3034808984

Category: Mathematics

Page: 626

View: 3758

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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)
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The Learning and Teaching of Geometry in Secondary Schools

A Modeling Perspective

Author: Pat Herbst,Taro Fujita,Stefan Halverscheid,Michael Weiss

Publisher: Taylor & Francis

ISBN: 1351973533

Category: Education

Page: 240

View: 8415

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IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.
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Foundations of Geometric Cognition

Author: Mateusz Hohol

Publisher: Routledge

ISBN: 0429509219

Category: Psychology

Page: 188

View: 5907

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The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.
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The Oxford Handbook of the History of Mathematics

Author: Eleanor Robson,Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191607444

Category: Mathematics

Page: 926

View: 1998

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This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
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Faiths Across Time: 5,000 Years of Religious History [4 Volumes]

5,000 Years of Religious History

Author: J. Gordon Melton

Publisher: ABC-CLIO

ISBN: 1610690265

Category: Reference

Page: 2023

View: 5416

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This monumental, four-volume reference overviews significant events and developments in religious history over the course of more than five millennia. • Provides interesting sidebars to entries on such topics as monotheism and the problem of evil, the construction of the Egyptian pyramids, Mesoamerican mythology, the legacy of Charlemagne, the lives of various religious thinkers and leaders, the Hundred Years' War, the indigenous religions of South Africa, the Second Great Awakening, Potala Palace in Tibet, and many others • Offers a sweeping chronological presentation of faith and religion over five millennia that enables readers to see the connections between historical events and the evolution of various belief systems • Includes an extensive selection of photos that helps readers visualize many of the topics discussed in the text
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Vita Mathematica

Historical Research and Integration with Teaching

Author: Ronald Calinger

Publisher: Cambridge University Press

ISBN: 9780883850978

Category: Mathematics

Page: 359

View: 4450

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Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching.
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Pomegranate

Anatomy of a Divine Remedy

Author: Hassan Amjad

Publisher: Lulu.com

ISBN: 1411662784

Category:

Page: 126

View: 372

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In this book, I share some of my enthusiasm as to why the pomegranate is a magnificient, trans-cultural, symbolic icon in medicine, health, and mythology.
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Vampires

A bite-sized history

Author: Judyth A McLeod

Publisher: Allen & Unwin

ISBN: 1742662579

Category: Social Science

Page: 240

View: 6446

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Vampires offers a bite-sized overview of the ever-mutating vampire, a phenomenon created by primal human fears of blood-sucking monsters. The book delves into ancient vampiric beliefs including the Chinese hopping vampire Jiangshi and Egyptian goddess Sekhmet, as well as Gothic horrors from the late Middle Ages. The evolution of vampires in literature, film and television is comprehensively covered, from the iconic Dracula tale, Stephen King's Salem's Lot to Stephenie Meyer's 'Twilight' series; Nosferatu, the first Hollywood take on vampires and modern films such as the Blade trilogy and New Moon; and popular TV shows including The Twilight Zone, True Blood and The Vampire Diaries.
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