Fractions Tilings And Geometry

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Fractions, Tilings, and Geometry

Author : Bowen Kerins
Publisher : American Mathematical Soc.
ISBN 13 : 1470440644
Total Pages : 172 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fractions, Tilings, and Geometry by : Bowen Kerins

Download or read book Fractions, Tilings, and Geometry written by Bowen Kerins and published by American Mathematical Soc.. This book was released on 2018-01-25 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Fractions, Tilings, and Geometry

Author : Bowen Kerins
Publisher :
ISBN 13 : 9781470443405
Total Pages : 172 pages
Book Rating : 4.4/5 (434 download)

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Book Synopsis Fractions, Tilings, and Geometry by : Bowen Kerins

Download or read book Fractions, Tilings, and Geometry written by Bowen Kerins and published by . This book was released on 2017 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tesse.

Geometry and Fractions with Color Tiles

Author : Barbara Bando Irvin
Publisher :
ISBN 13 : 9781569118658
Total Pages : 64 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Geometry and Fractions with Color Tiles by : Barbara Bando Irvin

Download or read book Geometry and Fractions with Color Tiles written by Barbara Bando Irvin and published by . This book was released on 1997 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry and Fractions with Color Tiles Activity Set

Author : Learning Resources, Incorporated
Publisher :
ISBN 13 : 9781569115190
Total Pages : pages
Book Rating : 4.1/5 (151 download)

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Book Synopsis Geometry and Fractions with Color Tiles Activity Set by : Learning Resources, Incorporated

Download or read book Geometry and Fractions with Color Tiles Activity Set written by Learning Resources, Incorporated and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractions and Geometry Through Menu Math

Author : Mary Townsend Smithey
Publisher :
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Fractions and Geometry Through Menu Math by : Mary Townsend Smithey

Download or read book Fractions and Geometry Through Menu Math written by Mary Townsend Smithey and published by . This book was released on 1989 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Shapes, Halves, and Symmetry

Author : Joan Akers
Publisher :
ISBN 13 : 9781572326569
Total Pages : 252 pages
Book Rating : 4.3/5 (265 download)

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Book Synopsis Shapes, Halves, and Symmetry by : Joan Akers

Download or read book Shapes, Halves, and Symmetry written by Joan Akers and published by . This book was released on 1998 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Shapes & Beginning Fractions

Author : Jo Ellen Moore
Publisher : Evan-Moor Educational Publishers
ISBN 13 : 9781557994493
Total Pages : 32 pages
Book Rating : 4.9/5 (944 download)

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Book Synopsis Geometric Shapes & Beginning Fractions by : Jo Ellen Moore

Download or read book Geometric Shapes & Beginning Fractions written by Jo Ellen Moore and published by Evan-Moor Educational Publishers. This book was released on 1997-04-17 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Substitution and Tiling Dynamics: Introduction to Self-inducing Structures

Author : Shigeki Akiyama
Publisher : Springer Nature
ISBN 13 : 3030576663
Total Pages : 456 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Substitution and Tiling Dynamics: Introduction to Self-inducing Structures by : Shigeki Akiyama

Download or read book Substitution and Tiling Dynamics: Introduction to Self-inducing Structures written by Shigeki Akiyama and published by Springer Nature. This book was released on 2020-12-05 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.

Handbook of Convex Geometry

Author : Bozzano G Luisa
Publisher : Elsevier
ISBN 13 : 0080934404
Total Pages : 769 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Convex Geometry by : Bozzano G Luisa

Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Geometry of Continued Fractions

Author : Oleg N. Karpenkov
Publisher : Springer Nature
ISBN 13 : 3662652773
Total Pages : 462 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Geometry of Continued Fractions by : Oleg N. Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg N. Karpenkov and published by Springer Nature. This book was released on 2022-05-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Discrete Geometry for Computer Imagery

Author : Christophe Reutenauer
Publisher : Springer Science & Business Media
ISBN 13 : 3642043968
Total Pages : 551 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Discrete Geometry for Computer Imagery by : Christophe Reutenauer

Download or read book Discrete Geometry for Computer Imagery written by Christophe Reutenauer and published by Springer Science & Business Media. This book was released on 2009-09-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.

Geometry of Continued Fractions

Author : Oleg Karpenkov
Publisher : Springer Science & Business Media
ISBN 13 : 3642393683
Total Pages : 409 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Fractions

Author : Olive Mary Mason
Publisher :
ISBN 13 :
Total Pages : 87 pages
Book Rating : 4.:/5 (216 download)

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Book Synopsis Fractions by : Olive Mary Mason

Download or read book Fractions written by Olive Mary Mason and published by . This book was released on 1981 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractions, Geometry, and Measurement

Author : Vicky Shiotsu
Publisher : Milliken Publishing Company
ISBN 13 : 0787742937
Total Pages : 16 pages
Book Rating : 4.7/5 (877 download)

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Book Synopsis Fractions, Geometry, and Measurement by : Vicky Shiotsu

Download or read book Fractions, Geometry, and Measurement written by Vicky Shiotsu and published by Milliken Publishing Company. This book was released on 2004-09-01 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Closely aligned with the national standards, this packet helps students review fractions, geometry, and measurement. Engaging formats and fun activities (including puzzles, riddles, and games) offer solid review opportunities. Answer key is included.

Geometry and Fractions

Author : Linda Cernak
Publisher : Milliken Publishing Company
ISBN 13 : 0787742880
Total Pages : 13 pages
Book Rating : 4.7/5 (877 download)

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Book Synopsis Geometry and Fractions by : Linda Cernak

Download or read book Geometry and Fractions written by Linda Cernak and published by Milliken Publishing Company. This book was released on 2004-09-01 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Closely aligned with the national standards, this packet helps students review geometry and fractions. Engaging formats and fun activities (including puzzles, riddles, and games) offer solid review opportunities. Answer key is included.

Geometry and Fractions with Pattern Blocks

Author : Barbara Bando Irvin
Publisher :
ISBN 13 : 9781569119754
Total Pages : 64 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Geometry and Fractions with Pattern Blocks by : Barbara Bando Irvin

Download or read book Geometry and Fractions with Pattern Blocks written by Barbara Bando Irvin and published by . This book was released on 1995 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 64-page blackline master book, complete with teaching notes and problem-solving activities for congruent and similar shapes, transformational geometry and fractions.

Discrete Geometry for Computer Imagery

Author : Srecko Brlek
Publisher : Springer
ISBN 13 : 3642043976
Total Pages : 551 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Discrete Geometry for Computer Imagery by : Srecko Brlek

Download or read book Discrete Geometry for Computer Imagery written by Srecko Brlek and published by Springer. This book was released on 2009-09-19 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.