The Geometry of Ancient Sites PDF Download

Author: Charles William Johnson
Publisher:
ISBN: 9781586161866
Category :
Languages : en
Pages : 153

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Author: Mark Vidler
Publisher: Inner Traditions
ISBN: 9781620554685
Category : Body, Mind & Spirit
Languages : en
Pages : 0

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Identifies the patterns of our planet’s design within the natural landscape • Explains the geometry inherent in the mountains and coasts on all continents • Reveals how ancient monuments were built to reflect and enhance the Earth’s design, often connecting sites around the world • Includes detailed maps that show the simple geometrical relationships among the world’s mountains, coastlines, islands, and ancient monuments From continent to continent across the globe, Mark Vidler and Catherine Young reveal that order is everywhere on Earth. On remote islands, soaring summits, and level deltas, they unveil natural topographic patterns related to pi, the golden ratio, and right-triangle geometry. And as the planet’s design emerges, it becomes clear that this hidden order in nature decided the location of ancient monuments the world over. Through detailed maps, Vidler and Young show how the locations of megalithic monuments reflect and enhance a natural pattern on the Earth that connects its major features. The rows of standing stones at Carnac in France, for example, point to the summits of Mount Everest and K2, and Angkor Wat in Cambodia is on a straight line joining Mount Kilimanjaro in Africa and the tip of Cape Comorin in India. The authors examine the geography of many islands and each continent, including Antarctica, to show how the highest peak on each landmass falls on a line connecting coastal extremes. They reveal how circles of standing stones and man-made mounds mark intersections of these lines. They explore the connection between the Nazca lines in Peru and the Amazon, Nile, and Ganges deltas and explain how the locations of the Giza pyramids, Stonehenge, and Machu Picchu are integrated into the natural design on Earth. As they uncover geometric patterns on the Earth line by line, point by point, the authors reveal how the world’s ancient monuments represent a form of transglobal communication that far predates the written word.

Author: Ken Taylor
Publisher: National Geographic Books
ISBN: 1786782707
Category : Social Science
Languages : en
Pages : 0

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Book Description
This book travels the world to explore over 60 archaeological sites that enshrine the remarkable achievements of ancient astronomers. In many cultures, an early understanding of the cosmos is expressed through architecture—stone circles that act as giant computers for the timing of eclipses or connections with the rising or setting of planets. The author’s focus ranges broadly—from the great stone circles of Europe to the pyramids of Egypt and the pyramid-temples of Central America, from the medicine wheels of North America to the carved monoliths of Easter Island. In part, however, the book’s value lies in its revelation of astronomical alignments in lesser-known structures, such as the vast sun clock of Goseck in Germany and the ancient rock art of Australia. The book is organized by key celestial events including lunar and solar eclipses, and features original artwork showing key alignments and the movements of the planets and stars. The book offers beautiful and fascinating insights into the mysteries of the ancient world—and a vision of mankind’s efforts to integrate our sense of spiritual belonging with the mysteries of space and time.

Author: Bartel L. van der Waerden
Publisher: Springer Science & Business Media
ISBN: 3642617794
Category : Mathematics
Languages : en
Pages : 236

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Book Description
Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation.

Author: T. A. Sarasvati Amma
Publisher: Motilal Banarsidass Publ.
ISBN: 9788120813441
Category : Geometry
Languages : en
Pages : 304

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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.

Author: J. L. Heilbron
Publisher: Oxford University Press
ISBN: 9780198506904
Category : History
Languages : en
Pages : 344

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Book Description
This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.

Author: Richard Heath
Publisher: Simon and Schuster
ISBN: 1644111195
Category : Body, Mind & Spirit
Languages : en
Pages : 465

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Book Description
Reveals how the number science found in ancient sacred monuments reflects wisdom transmitted from the angelic orders • Explains how the angels transmitted megalithic science to early humans to further our conscious development • Decodes the angelic science hidden in a wide range of monuments, including Carnac in Brittany, the Great Pyramid in Egypt, early Christian pavements, the Hagia Sophia in Istanbul, Stonehenge in England, and the Kaaba in Mecca • Explores how the number science behind ancient monuments gave rise to religions and spiritual practices The angelic mind is founded on a deep understanding of number and the patterns they produce. These patterns provided a constructive framework for all manifested life on Earth. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us. Examining the angelic science of number first manifested on Earth in the Stone Age, Richard Heath reveals how the resulting development of human consciousness was no accident: just as the angels helped create the Earth’s environment, humans were then evolved to make the planet self-aware. To develop human minds, the angels transmitted their own wisdom to humanity through a numerical astronomy that counted planetary and lunar time periods. Heath explores how this early humanity developed an expert understanding of sacred number through astronomical geometries, leading to the unified range of measures employed in their observatories and later in cosmological monuments such as the Giza Pyramids and Stonehenge. The ancient Near East transformed megalithic science into our own mathematics of notational arithmetic and trigonometry, further developing the human mind within the early civilizations. Heath decodes the angelic science hidden within a wide range of monuments and sites, including Carnac in Brittany, the Great Pyramid in Egypt, Teotihuacan in Mexico, early Christian pavements, the Hagia Sophia in Istanbul, and the Kaaba in Mecca. Exploring the techniques used to design these monuments, he explains how the number science behind them gave rise to ancient religions and spiritual practices. He also explores the importance of lunar astronomy, first in defining a world suitable for life and then in providing a subject accessible to pre-arithmetic humans, for whom the Moon was a constant companion.

Author: Christoph J. Scriba
Publisher: Birkhäuser
ISBN: 3034808984
Category : Mathematics
Languages : en
Pages : 638

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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)

Author: Paul W. Hightower
Publisher: Enslow Publishing, LLC
ISBN: 9780766034099
Category : Juvenile Nonfiction
Languages : en
Pages : 118

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"A biography of ancient Greek mathematician Euclid, known as the father of geometry and author of the mathematics textbook Elements"--Provided by publisher.

Author: W.R. Knorr
Publisher: Springer Science & Business Media
ISBN: 1461236908
Category : Mathematics
Languages : en
Pages : 850

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For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.