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This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity.

Fine Arts - General --- Art, Architecture & Applied Arts --- Geometry. --- Mathematics. --- Polytopes. --- Discrete mathematics. --- Mathematics in Art and Architecture. --- Discrete Mathematics. --- Popular Science in Mathematics. --- Mathematics --- Euclid's Elements --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Hyperspace --- Topology --- Math --- Science

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Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Combinatorial analysis. --- Geometry, Algebraic. --- Combinatorial topology. --- Algebraic geometry --- Combinatorics --- Mathematics. --- Algebra. --- Convex geometry. --- Discrete geometry. --- Topology. --- Discrete mathematics. --- Discrete Mathematics. --- Convex and Discrete Geometry. --- Mathematical analysis --- Complexes --- Topology --- Geometry --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Discrete mathematics --- Convex geometry . --- Combinatorial geometry --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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This book constitutes the thoroughly refereed conference proceedings of the 9th International Workshop on Algorithms and Computation, WALCOM 2015, held in Dhaka, Bangladesh, in February 2015. The 26 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 85 submissions. The papers are organized in topical sections on approximation algorithms, data structures and algorithms, computational geometry, combinatorial algorithms, distributed and online algorithms, graph drawing and algorithms, combinatorial problems and complexity, and graph enumeration and algorithms.

Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Math Applications in Computer Science. --- Symbolic and Algebraic Manipulation. --- Computer Graphics. --- Algorithms. --- Computer science. --- Computer software. --- Computational complexity. --- Algebra --- Computer graphics. --- Informatique --- Logiciels --- Complexité de calcul (Informatique) --- Algèbre --- Infographie --- Algorithmes --- Data processing. --- Engineering & Applied Sciences --- Computer Science --- Computer science --- Mathematics. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer mathematics --- Discrete mathematics --- Algorism --- Arithmetic --- Informatics --- Science --- Digital techniques --- Mathematics --- Foundations --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Discrete mathematics. --- Mathematical Applications in Computer Science. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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This book constitutes the proceedings of the 9th International Workshop on Frontiers in Algorithmics, FAW 2015, held in Guilin, China, in July 2015. The 28 papers presented in this volume were carefully reviewed and selected from 65 submissions. They deal with graph algorithms, approximation algorithms, combinatorial optimization, parameterized algorithms, and online algorithms.

Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Computation by Abstract Devices. --- Computer science. --- Computer software. --- Computational complexity. --- Informatique --- Logiciels --- Complexité de calcul (Informatique) --- Computer Science --- Engineering & Applied Sciences --- Computers. --- Algorithms. --- Computer science --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Informatics --- Science --- Mathematics --- Foundations --- Complexity, Computational --- Software, Computer --- Computer algorithms --- Computer science—Mathematics. --- Discrete mathematics. --- Theory of Computation. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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This book constitutes the refereed conference proceedings of the 9th International Conference on Algorithms and Complexity, CIAC 2015, held in Paris, France, in May 2015. The 30 revised full papers presented were carefully reviewed and selected from 93 submissions and are presented together with 2 invited papers. The papers present original research in the theory and applications of algorithms and computational complexity.

Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Data Structures. --- Computer science. --- Data structures (Computer science). --- Computer software. --- Computational complexity. --- Informatique --- Structures de données (Informatique) --- Logiciels --- Complexité de calcul (Informatique) --- Engineering & Applied Sciences --- Computer Science --- Algorithms. --- Computer science --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Informatics --- Science --- Mathematics --- Foundations --- Data structures (Computer scienc. --- Data structures (Computer science) --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- Computer algorithms --- Computer science—Mathematics. --- Discrete mathematics. --- Artificial intelligence—Data processing. --- Data Science. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis