Form And Clarity In Euclids Elements

Author : Anna-Maria Gasser
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110670593
Total Pages : 676 pages
Book Rating : 4.92/5 ( download)

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Download or read book Form and Clarity in Euclid’s ›Elements‹ written by Anna-Maria Gasser and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: As of yet, the remarkable and highly influential textual form of Euclidean mathematics has not been considered from a literary-aesthetic perspective. By its extreme standardization and seeming non-literariness it appears to defy such an approach. This book nonetheless attempts precisely a literary-aesthetic study of the language and style of Euclid’s Elements, focusing on book I. It aims to find out what is literary about the form and what motivates this form as form. In doing so, it employs the concept of clarity, asking: How is the textual form related to logical and communicative clarity? That is, how far is the omnipresent standardization necessary for the accomplishment and successful communication of the proofs? Based on a close analysis of the standardization at all levels of the text (lexicon, grammar, structure, and especially diagram), it argues that the textual form of the Elements is standardized beyond logical-communicative purposes, and that it is in this sense ‘aesthetic’. The book exposes the unexpected literary dimension of Euclid’s Elements, provides a new interpretation of the peculiar form of the work, and offers a model for determining the role of clarity (not only) in Greek theoretical mathematics.

Author : Anna-Maria Gasser
Publisher : de Gruyter
ISBN 13 : 9783110670332
Total Pages : 0 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Form and Clarity in Euclid's ›Elements‹ written by Anna-Maria Gasser and published by de Gruyter. This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the form of Euclid's Elements from a literary-aesthetic perspective. It asks what is 'literary' about the seemingly non-literary form of the proofs, and what motivates this form as form. Based on a detailed analysis of the e

Author : Proclus
Publisher : Princeton University Press
ISBN 13 : 0691214670
Total Pages : 428 pages
Book Rating : 4.72/5 ( download)

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Download or read book Proclus written by Proclus and published by Princeton University Press. This book was released on 2020-06-30 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Proclus: A Commentary on the First Book of Euclid's Elements, will be forthcoming.

Author : David Berlinski
Publisher : Basic Books
ISBN 13 : 0465038638
Total Pages : 193 pages
Book Rating : 4.33/5 ( download)

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Download or read book The King of Infinite Space written by David Berlinski and published by Basic Books. This book was released on 2014-04-08 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic -- and the mathematical statements he and others built from it -- have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.

Author : William Dunham
Publisher : Penguin Books
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.95/5 ( download)

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Download or read book Journey Through Genius written by William Dunham and published by Penguin Books. This book was released on 1991-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov

Author : Tristan Needham
Publisher : Princeton University Press
ISBN 13 : 0691203695
Total Pages : 530 pages
Book Rating : 4.90/5 ( download)

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Download or read book Visual Differential Geometry and Forms written by Tristan Needham and published by Princeton University Press. This book was released on 2021-07-13 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Author : Markus Asper
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111314537
Total Pages : 312 pages
Book Rating : 4.32/5 ( download)

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Download or read book Coming to Terms written by Markus Asper and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-12-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Terminologies present various challenges to their inventors and to their users, ranging from epistemic adequacy over linguistic concerns to matters of strategy and group construction. With respect to historical terminologies, however, research has been dominated by linguistic approaches. Breaking new ground, Coming to Terms collects eleven articles that combine an interest in the history of knowledge, mostly ancient Greek, with research on scientific terminologies. They all share an interest in terminological practices, that is, questions such as how and when to coin a term and then what to do with it. Among the fields discussed are astronomy, the Roman surveyors, Aristotelian science, Renaissance and modern biology, contemporary medicine, ancient Chinese philosophy, 20th-century physics, and colonial linguistics. Confronting ancient with modern terminologies, the collection intends to test integrative interpretive approaches. Thus, the collection documents how rich ancient (and modern) terminologies are and shows that they are, beyond lexicography, worth being studied per se.

Author : David Hilbert
Publisher : Read Books Ltd
ISBN 13 : 1473395941
Total Pages : 139 pages
Book Rating : 4.47/5 ( download)

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Download or read book The Foundations of Geometry written by David Hilbert and published by Read Books Ltd. This book was released on 2015-05-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

Author : Leonhard Euler
Publisher :
ISBN 13 :
Total Pages : 960 pages
Book Rating : 4.19/5 ( download)

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Download or read book Elements of Algebra written by Leonhard Euler and published by . This book was released on 1810 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Benjamin Wardhaugh
Publisher : Princeton University Press
ISBN 13 : 0691235767
Total Pages : 416 pages
Book Rating : 4.69/5 ( download)

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Download or read book Encounters with Euclid written by Benjamin Wardhaugh and published by Princeton University Press. This book was released on 2023-11-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. 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. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.