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Geometry --- History --- Famous problems --- -Geometry --- -Mathematics --- Euclid's Elements --- Problems, Famous --- -History --- Famous problems in geometry --- Problems, Famous, in geometry --- Geometry - History --- Geometry - Famous problems --- Histoire des mathematiques --- Geometrie --- Constructions geometriques --- Antiquite --- Histoire

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514.12 --- #WBIB:dd.Lic.L.De Busschere --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Geometry --- Famous problems in geometry --- Problems, Famous, in geometry --- Famous problems --- Problems, Famous --- Géométrie --- Famous problems. --- Problèmes classiques. --- Problèmes classiques --- Géométrie --- Problèmes classiques --- Problèmes classiques.

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Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the constructibility of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals, and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of groups, fields, or abstract algebra is assumed. Notable topics treated along this route include the transcendence of e and of pi, cyclotomic polynomials, polynomials over the integers, Hilbert's, irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems. Field Theory and its Classical Problems is a winner of the MAA Edwin Beckenbach Book Prize for excellence in mathematical exposition.

Equations --- Geometry --- Famous problems in geometry --- Problems, Famous, in geometry --- Algebra --- Numerical solutions. --- Famous problems. --- Problems, Famous --- Graphic methods --- Algebraic fields. --- Radical theory. --- Associative rings --- Commutative rings --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra)

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Icons of mathematics are certain geometric diagrams that play a crucial role in visualizing mathematical proofs, and in the book the authors present 20 of them and explore the mathematics that lies within and that can be created. The authors devote a chapter to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus, and puzzles from recreational mathematics.

Geometry --- Geometrical constructions. --- Generation of geometric forms. --- Proof theory. --- Mathematical notation. --- Geometrical drawing. --- Geometry, Plane. --- Visualization. --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Plane geometry --- Mathematical drawing --- Plans --- Drawing --- Mechanical drawing --- Projection --- Mathematical symbols --- Mathematics --- Notation, Mathematical --- Logic, Symbolic and mathematical --- Geometric forms, Generation of --- Geometrical drawing --- Geometry, Descriptive --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Famous problems in geometry --- Problems, Famous, in geometry --- Famous problems. --- Symbols --- Problems, Famous

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"The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English. This book is essential reading for teachers and researchers who may be out of touch with the latest developments in computational logic. It will also be useful in any undergraduate course that teaches practical thinking, problem solving or communication skills. Its informal presentation makes the book accessible to readers from any background, but optional, more formal, chapters are also included for those who are more technically oriented"--

Computational intelligence --- Logic, Symbolic and mathematical --- Rhetoric --- Communication --- Reasoning --- Critical thinking --- Famous problems --- Mathematics --- Philosophy --- Computational intelligence. --- Critical thinking. --- Reasoning. --- Computers --- Philosophy. --- Famous problems. --- Mathematics. --- Natural Language Processing --- Critical reflection --- Reflection (Critical thinking) --- Reflection process --- Reflective thinking --- Thinking, Critical --- Thinking, Reflective --- Thought and thinking --- Reflective learning --- Argumentation --- Ratiocination --- Reason --- Judgment (Logic) --- Logic --- Language and languages --- Speaking --- Authorship --- Expression --- Style, Literary --- Famous problems in symbolic and mathematical logic --- Problems, Famous, in symbolic and mathematical logic --- Intelligence, Computational --- Artificial intelligence --- Natural Language Processing. --- Literary style --- Soft computing --- Evaluative thinking --- Information Technology --- Computer Science (Hardware & Networks) --- Logic, Symbolic and mathematical - Famous problems --- Rhetoric - Mathematics --- Communication - Philosophy