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Author: Anna-Maria Gasser
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110670593
Category : History
Languages : en
Pages : 676
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Book Description
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: Walter de Gruyter GmbH & Co KG
ISBN: 3110670593
Category : History
Languages : en
Pages : 676
Get Book Here
Book Description
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: 9783110670332
Category : History
Languages : en
Pages : 0
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Book Description
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: 0691214670
Category : Philosophy
Languages : en
Pages : 428
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Book Description
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: 0465038638
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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:
Category : Biography & Autobiography
Languages : en
Pages : 324
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Book Description
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: 0691203695
Category : Mathematics
Languages : en
Pages : 530
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Book Description
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: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 0387226761
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Author: Markus Asper
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111314537
Category : History
Languages : en
Pages : 312
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Book Description
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: Martin H. Weissman
Publisher: American Mathematical Soc.
ISBN: 1470463717
Category : Education
Languages : en
Pages : 341
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Book Description
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Author: Leonhard Euler
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 960
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Book Description
