Search Results for encounters-with-euclid

Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.

Author: Benjamin Wardhaugh

Publisher: Princeton University Press

ISBN: 9780691211695

Category: Mathematics

Page: 416

View: 280

In this lively and informative book, Benjamin Wardhaugh explains how Euclid's text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.
2021-07-06 By Benjamin Wardhaugh

Euclid Between Man, Cosmos, and God Michael J. Sauter ... I propose, however, to read Hobbes against the disciplinary grain and thereby to understand his political thought as a product of his encounters with Euclidean geometry.

Author: Michael J. Sauter

Publisher: University of Pennsylvania Press

ISBN: 9780812295559

Category: Science

Page: 344

View: 185

In The Spatial Reformation, Michael J. Sauter offers a sweeping history of the way Europeans conceived of three-dimensional space, including the relationship between Earth and the heavens, between 1350 and 1850. He argues that this "spatial reformation" provoked a reorganization of knowledge in the West that was arguably as important as the religious Reformation. Notably, it had its own sacred text, which proved as central and was as ubiquitously embraced: Euclid's Elements. Aside from the Bible, no other work was so frequently reproduced in the early modern era. According to Sauter, its penetration and suffusion throughout European thought and experience call for a deliberate reconsideration not only of what constitutes the intellectual foundation of the early modern era but also of its temporal range. The Spatial Reformation contends that space is a human construct: that is, it is a concept that arises from the human imagination and gets expressed physically in texts and material objects. Sauter begins his examination by demonstrating how Euclidean geometry, when it was applied fully to the cosmos, estranged God from man, enabling the breakthrough to heliocentrism and, by extension, the discovery of the New World. Subsequent chapters provide detailed analyses of the construction of celestial and terrestrial globes, Albrecht Dürer's engraving Melencolia, the secularization of the natural history of the earth and man, and Hobbes's rejection of Euclid's sense of space and its effect on his political theory. Sauter's exploration culminates in the formation of a new anthropology in the eighteenth century that situated humanity in reference to spaces and places that human eyes had not actually seen. The Spatial Reformation illustrates how these disparate advancements can be viewed as resulting expressly from early modernity's embrace of Euclidean geometry.
2018-11-21 By Michael J. Sauter

Euclid's influence Determining to what degree Euclid's 'Elements' influenced Indian mathematics is a difficult ... However, as already mentioned, the encounters with Euclid (in Arabic or Persian translation) did not result in the ...

Author: Christoph J. Scriba

Publisher: Birkhäuser

ISBN: 9783034808989

Category: Mathematics

Page: 626

View: 870

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)
2015-04-22 By Christoph J. Scriba

... as he consistently structures the reality he encounters in Euclidean terms . The most intriguing consequence of Stephen's Euclidean worldview , however , appears in his discussion of aesthetics in the fifth chapter ( P 204-15 ) .

Author: Thomas Jackson Rice

Publisher: University of Illinois Press

ISBN: 0252065832

Category: Literary Criticism

Page: 228

View: 472

Joyce, Chaos, and Complexity studies the manifold relations among twentieth-century mathematics and Science, James Joyce's fiction, and the critical reception of Joyce's work. Calling for profound reassessments, Thomas Jackson Rice compellingly argues that Joyce's work resists postmodernist approaches of ambiguity: Joyce never abandoned his conviction that reality exists, regardless of the human ability to represent it. Placing Joyce in his cultural context, Rice first provocatively traces the previously unacknowledged formative influence of Euclidean and non-Euclidean geometries on Dubliners and A Portrait of the Artist as a Young Man. He then demonstrates that, when later innovations in science transformed entire worldviews, Joyce recognized conventional literary modes of representation as offering merely arbitrary constructions of this new reality. Joyce responded to these developmeats in Ulysses by experimenting with perspective, embedding design, and affirming the existence of reality. Rice contends that Ulysses is a precursor to the multiple tensions of chaos theory; likewise, chaos theory can serve as a model for understanding Ulysses. In Finnegans Wake Joyce consummates his vision and anticipates the theories of complexity science through a dynamic approximation of reality.

Although it is possible to read Aubrey's anecdote as suggesting that this was Hobbes's first encounter with Euclid, it is unlikely that this was the case.6 What appealed to Hobbes in this instance was the effect that Euclid's method ...

Author: Ioannis D. Evrigenis

Publisher: Cambridge University Press

ISBN: 9780521513722

Category: Political Science

Page: 313

View: 511

Hobbes's concept of the natural condition of mankind became an inescapable point of reference for subsequent political thought, shaping the theories of emulators and critics alike, and has had a profound impact on our understanding of human nature, anarchy, and international relations. Yet, despite Hobbes's insistence on precision, the state of nature is an elusive concept. Has it ever existed and, if so, for whom? Hobbes offered several answers to these questions, which taken together reveal a consistent strategy aimed at providing his readers with a possible, probable, and memorable account of the consequences of disobedience. This book examines the development of this powerful image throughout Hobbes's works, and traces its origins in his sources of inspiration. The resulting trajectory of the state of nature illuminates the ways in which Hobbes employed a rhetoric of science and a science of rhetoric in his relentless pursuit of peace.
2014-07-14 By Ioannis D. Evrigenis

In three dimensions, such as on a sphere, one can encounter triangles with more than 180 degrees. ... (Incidentally, this theory was confirmed to 14 decimal places in 1993.108) BEYOND EUCLID After the Bible, Euclid's Elements was ...

Author: Chuck Missler

Publisher: Koinonia House

ISBN: 9781578215096

Category: Body, Mind & Spirit


View: 267

1997-07-30 By Chuck Missler

Ramus reprised this anecdote when recounting the life of Euclid later in the Prooemium. He expanded the encounter between king and geometer far beyond Proclus's brief notice. Ptolemy, he tells the reader, had heard report of Euclid's ...

Author: Robert Goulding

Publisher: Springer Science & Business Media

ISBN: 9789048135424

Category: Science

Page: 5

View: 477

Why should mathematics, the purest of sciences, have a history? Medieval mathematicians took little interest in the history of their discipline. Yet in the Renaissance the history of mathematics flourished. This book explores how Renaissance scholars recovered and reconstructed the origins of mathematics by tracing its invention in prehistoric Antiquity, its development by the Greeks, and its transmission to modern Europe via the works of Euclid, Theon and Proclus. The principal architects of this story -- the French philosopher and University of Paris reformer Peter Ramus, and his critic, the young Oxford astronomy lecturer Henry Savile – worked out diametrically opposed models for the development of the mathematical arts, models of historical progress and decline which mirrored each scholar’s larger convictions about the nature of mathematical thinking, the purpose of the modern university, and the potential of the human mind. In their hands, the obscure story of mathematical history became a site of contention over some of the most pressing philosophical and pedagogical debates of the sixteenth century.
2010-06-09 By Robert Goulding

In E* there is also a counterpart to the group of congruence transformations of the Euclidean plane. There is, for instance, a bijection of E* that preserves ... It turns out that all of Euclid's axioms hold in E* except the axiom of ...

Author: Lars Garding

Publisher: Springer Science & Business Media

ISBN: 9781461596417

Category: Mathematics

Page: 270

View: 254

Trying to make mathematics understandable to the general public is a very difficult task. The writer has to take into account that his reader has very little patience with unfamiliar concepts and intricate logic and this means that large parts of mathematics are out of bounds. When planning this book, I set myself an easier goal. I wrote it for those who already know some mathematics, in particular those who study the subject the first year after high school. Its purpose is to provide a historical, scientific, and cultural frame for the parts of mathematics that meet the beginning student. Nine chapters ranging from number theory to applications are devoted to this program. Each one starts with a historical introduction, continues with a tight but complete account of some basic facts and proceeds to look at the present state of affairs including, if possible, some recent piece of research. Most of them end with one or two passages from historical mathematical papers, translated into English and edited so as to be understandable. Sometimes the reader is referred back to earlier parts of the text, but the various chapters are to a large extent independent of each other. A reader who gets stuck in the middle of a chapter can still read large parts of the others. It should be said, however, that the book is not meant to be read straight through.
2012-12-06 By Lars Garding

them Euclid's two tacit assumptions regarding circles , referred to above . This leaves untouched , however , the difficulty which the student encounters with Euclid I , 5 ( the pons asinorum ) , and with the introduction to the study ...



ISBN: PRNC:32101080166414

Category: Electronic journals

Page: 192

View: 953

1920 By

A beginner first encounters this inEuclid I.6, whereit isshownthat iftwoangles of a triangle are equal, ... The modern wayistotake as axioms certain assumptions of a geometrical nature,more restricted than Euclid's common notions.

Author: Julian Lowell Coolidge

Publisher: Courier Corporation

ISBN: 9780486158532

Category: Mathematics

Page: 480

View: 759

Full, authoritative history of the techniques for dealing with geometric equations covers development of projective geometry from ancient to modern times, explaining the original works. 1940 edition.
2013-02-27 By Julian Lowell Coolidge