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Geometria convexa --- Funcions convexes --- Convex geometry. --- Convex functions --- Functions, Convex --- Functions of real variables --- Geometry
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Convex geometry. --- Monoids. --- Semigroups --- Geometry --- Geometria convexa --- Monoides --- Semigrups --- Convexitat geomètrica --- Geometria --- Conjunts convexos --- Funcions convexes
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Convex geometry. --- Convex functions --- Functions, Convex --- Functions of real variables --- Geometry --- Geometria convexa --- Funcions convexes --- Funcions de variables complexes --- Funcions còncaves --- Convexitat geomètrica --- Geometria --- Conjunts convexos
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Àlgebres associatives --- Funcions convexes --- Funcions de variables complexes --- Funcions còncaves --- Geometria convexa --- Àlgebra --- Grups de Brauer --- Àlgebres de Frobenius --- Teoria de la dimensió (Àlgebra) --- Associative algebras. --- Convex functions --- Algebras, Associative --- Algebra --- Functions, Convex --- Functions of real variables --- Convex functions.
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Geometria --- Matemàtica --- Congruències (Geometria) --- Dibuix lineal --- Envolupants (Geometria) --- Esfera --- Geometria algebraica --- Geometria computacional --- Geometria conforme --- Geometria convexa --- Geometria de l'espai --- Geometria diferencial --- Geometria euclidiana --- Porismes --- Programació geomètrica --- Ràtio i proporció --- Similitud (Geometria) --- Teorema de Pitàgores --- Transformacions (Matemàtica) --- Trigonometria --- Geometria en l'art --- Geometry. --- Mathematics --- Euclid's Elements
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Poliedres --- Geometria --- Matemàtica --- Congruències (Geometria) --- Dibuix lineal --- Envolupants (Geometria) --- Esfera --- Geometria algebraica --- Geometria computacional --- Geometria conforme --- Geometria convexa --- Geometria de l'espai --- Geometria diferencial --- Geometria euclidiana --- Porismes --- Programació geomètrica --- Ràtio i proporció --- Similitud (Geometria) --- Teorema de Pitàgores --- Transformacions (Matemàtica) --- Trigonometria --- Geometria en l'art --- Topologia --- Geometry. --- Geometry --- Polyhedra. --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Mathematics --- Euclid's Elements
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Geometry.. --- Mathematics.. --- Science.. --- Natural science --- Natural sciences --- Science of science --- Sciences --- Math --- Science --- Mathematics --- Euclid's Elements --- Science. --- Geometria --- Matemàtica --- Congruències (Geometria) --- Dibuix lineal --- Envolupants (Geometria) --- Esfera --- Geometria algebraica --- Geometria computacional --- Geometria conforme --- Geometria convexa --- Geometria de l'espai --- Geometria diferencial --- Geometria euclidiana --- Porismes --- Programació geomètrica --- Ràtio i proporció --- Similitud (Geometria) --- Teorema de Pitàgores --- Transformacions (Matemàtica) --- Trigonometria --- Geometria en l'art
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Geometry. --- Geometry --- Polyhedra. --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Mathematics --- Euclid's Elements --- Poliedres --- Geometria --- Matemàtica --- Congruències (Geometria) --- Dibuix lineal --- Envolupants (Geometria) --- Esfera --- Geometria algebraica --- Geometria computacional --- Geometria conforme --- Geometria convexa --- Geometria de l'espai --- Geometria diferencial --- Geometria euclidiana --- Porismes --- Programació geomètrica --- Ràtio i proporció --- Similitud (Geometria) --- Teorema de Pitàgores --- Transformacions (Matemàtica) --- Trigonometria --- Geometria en l'art --- Topologia
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This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Mathematics. --- Geometry. --- Geometry --- Mathematics --- Euclid's Elements --- Math --- Science --- Geometria --- Matemàtica --- Congruències (Geometria) --- Dibuix lineal --- Envolupants (Geometria) --- Esfera --- Geometria algebraica --- Geometria computacional --- Geometria conforme --- Geometria convexa --- Geometria de l'espai --- Geometria diferencial --- Geometria euclidiana --- Porismes --- Programació geomètrica --- Ràtio i proporció --- Similitud (Geometria) --- Teorema de Pitàgores --- Transformacions (Matemàtica) --- Trigonometria --- Geometria en l'art --- Group theory. --- Group Theory and Generalizations. --- Mathematics Education. --- Study and teaching . --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra
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Equacions de Lagrange --- Funcions convexes --- Integració numèrica --- Problemes de contorn --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Karman --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Quadratura mecànica --- Anàlisi numèrica --- Integrals definides --- Interpolació (Matemàtica) --- Funcions còncaves --- Geometria convexa --- Equació de D'Alembert --- Equacions d'Euler-Lagrange --- Euler-Lagrange (Equacions) --- Lagrange (Equacions) --- Equacions de Von Kármán --- Differential equations. --- Physics. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.91 Differential equations --- Differential equations
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