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Author: Nathaniel Miller
Publisher: Center for the Study of Language and Information Publica Tion
ISBN:
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
Author: Nathaniel Miller
Publisher: Center for the Study of Language and Information Publica Tion
ISBN:
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
Author: Dave Barker-Plummer
Publisher: Springer Science & Business Media
ISBN: 3540356231
Category : Computers
Languages : en
Pages : 313
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Book Description
Proceedings of the 4th International Conference on Theory and Application of Diagrams, Stanford, CA, USA in June 2006. 13 revised full papers, 9 revised short papers, and 12 extended abstracts are presented together with 2 keynote papers and 2 tutorial papers. The papers are organized in topical sections on diagram comprehension by humans and machines, notations: history, design and formalization, diagrams and education, reasoning with diagrams by humans and machines, and psychological issues in comprehension, production and communication.
Author: Euclid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 544
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Book Description
"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Author: Gem Stapleton
Publisher: Springer
ISBN: 3540877304
Category : Computers
Languages : en
Pages : 455
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Book Description
Diagrams is an international and interdisciplinary conference series, covering all aspects of research on the theory and application of diagrams. Recent technological advances have enabled the large-scale adoption of d- grams in a diverse range of areas. Increasingly sophisticated visual represen- tions are emerging and, to enable e?ective communication, insight is required into how diagrams are used and when they are appropriate for use. The per- sive, everyday use of diagrams for communicating information and ideas serves to illustrate the importance of providing a sound understanding of the role that diagrams can, and do, play. Research in the ?eld of diagrams aims to improve our understanding of the role of diagrams, sketches and other visualizations in communication, computation, cognition, creative thought, and problem solving. These concerns have triggered a surge of interest in the study of diagrams. The study of diagrammatic communication as a whole must be pursued as an interdisciplinary endeavour.Diagrams 2008 was the ?fth event in this conf- ence series, which was launched in Edinburghduring September 2000.Diagrams attracts a large number of researchers from virtually all related ?elds, placing the conference as a major international event in the area. Diagrams is the only conference that provides a united forum for all areas that are concerned with the study of diagrams: for example, architecture, - ti?cial intelligence, cartography, cognitive science, computer science, education, graphicdesign,historyofscience,human-computerinteraction,linguistics,logic, mathematics,philosophy,psychology,andsoftwaremodelling.Weseeissuesfrom all of these ?elds discussed in the papers collected in the present volume.
Author: Philip T. Cox
Publisher: Springer
ISBN: 3642312233
Category : Computers
Languages : en
Pages : 370
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Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Theory and Application of Diagrams, Diagrams 2012, held in Canaterbury, UK, in July 2012. The 16 long papers, 6 short papers and 21 poster abstracts presented were carefully reviewed and selected from 83 submissions. The papers are organized in keynotes, tutorial, workshops, graduate student symposium and topical sections on psychological and cognitive issues, diagram layout, diagrams and data analysis, Venn and Euler diagrams, reasoning with diagrams, investigating aesthetics, applications of diagrams.
Author: Charles L. Dodgson
Publisher: Legare Street Press
ISBN: 9781015505162
Category : History
Languages : en
Pages : 0
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Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Euclid
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 558
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Book Description
Author: Benjamin Wardhaugh
Publisher: Princeton University Press
ISBN: 0691235767
Category : Mathematics
Languages : en
Pages : 416
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Book Description
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.
Author: Paolo C. Biondi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110347776
Category : Philosophy
Languages : en
Pages : 544
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Book Description
Induction, which involves a leap from the particular to the universal, has always been a puzzling phenomenon for those attempting to investigate the origins of knowledge. Although traditionally accepted as the engine of first principles, the authority of inductive reasoning has been undermined in the modern age by empiricist criticisms that derive notably from Hume, who insisted that induction is an invalid line of reasoning that ends in unreliable future predictions. The present volume challenges this Humean orthodoxy. It begins with a thorough consideration of Hume’s original position and continues with a series of state-of-the-art essays that critique the received view while offering positive alternatives. The experts assembled here draw on a perennial historical tradition that stretches as far back as Socrates and extends through such luminaries as Aristotle, Aquinas, Whewell, Goethe, Lonergan, and Rescher. They inquire into the creative moment of intellectual insight that makes induction possible, consider relevant episodes from the history of science, advance scholarly exegeses of historical interpretations of inductive reasoning, and reflect critically on the scientific and logical ramifications of epistemological and metaphysical realism.
Author: Mateja Jamnik
Publisher: Springer
ISBN: 3319423339
Category : Computers
Languages : en
Pages : 306
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Book Description
This book constitutes the refereed proceedings of the 9th InternationalConference on the Theory and Application of Diagrams, Diagrams 2016,held in Philadelphia, PA, USA, in August 2016. The 12 revised full papers and 11 short papers presented together with 5 posters were carefully reviewed and selected from 48 submissions. The papers are organized in the following topical sections: cognitive aspects of diagrams; logic and diagrams; Euler and Venn diagrams; diagrams and education; design principles for diagrams; diagrams layout.
