Studies in the Theory and Applications of Diagrams – serie
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2 produkter
2 produkter
Euclid and His Twentieth Century Rivals
Diagrams in the Logic of Euclidean Geometry
Häftad, Engelska, 2007
228 kr
Skickas inom 5-8 vardagar
Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to his use of diagrams. In "Euclid and His Twentieth-Century Rivals", Nathaniel Miller discusses the history of such 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.
235 kr
Skickas inom 5-8 vardagar
Why are diagrams sometimes so useful, facilitating our understanding and thinking, while at other times they can be unhelpful and even misleading? Drawing on a comprehensive survey of modern research in philosophy, logic, artificial intelligence, cognitive psychology, and graphic design, Semantic Properties of Diagrams and Their Cognitive Potentials reveals the systematic reasons for this dichotomy, showing that the cognitive functions of diagrams are rooted in the characteristic ways they carry information. In analyzing the logical mechanisms behind the relative efficacy of diagrammatic representation, Atsushi Shimojima provides deep insight into the crucial question: What makes a diagram a diagram?