Fractions Tilings And Geometry

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Fractions, Tilings, and Geometry

Author : Bowen Kerins
Publisher : American Mathematical Soc.
ISBN 13 : 1470440644
Total Pages : 157 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 157 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:

Algebra and Tiling

Author : Sherman Stein
Publisher : Cambridge University Press
ISBN 13 : 9780883850282
Total Pages : 236 pages
Book Rating : 4.8/5 (52 download)

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Book Synopsis Algebra and Tiling by : Sherman Stein

Download or read book Algebra and Tiling written by Sherman Stein and published by Cambridge University Press. This book was released on 1994 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.

Miles of Tiles

Author : Charles Radin
Publisher : American Mathematical Soc.
ISBN 13 : 082181933X
Total Pages : 134 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Miles of Tiles by : Charles Radin

Download or read book Miles of Tiles written by Charles Radin and published by American Mathematical Soc.. This book was released on 1999 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative.

The Tiling Book

Author : Colin Adams
Publisher : American Mathematical Society
ISBN 13 : 1470474611
Total Pages : 310 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Tiling Book by : Colin Adams

Download or read book The Tiling Book written by Colin Adams and published by American Mathematical Society. This book was released on 2023-08-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

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:

Fractions: To Be Continued

Author : Bowen Kerins
Publisher : American Mathematical Soc.
ISBN 13 : 1470462931
Total Pages : 126 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fractions: To Be Continued by : Bowen Kerins

Download or read book Fractions: To Be Continued written by Bowen Kerins and published by American Mathematical Soc.. This book was released on 2021-09-17 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the eighth book in the Teacher Program Series. Each book includes a full course in a mathematical focus topic. The topic for this book is the study of continued fractions, including important results involving the Euclidean algorithm, the golden ratio, and approximations to rational and irrational numbers. The course includes 14 problem sets designed for low-threshold, high-ceiling access to the topic, building on one another as the concepts are explored. The book also includes solutions for all the main problems and detailed facilitator notes for those wanting to use this book with students at any level. The course is based on one delivered at the Park City Math Institute in Summer 2018.

Algebra and Tiling: Homorphisms in the Service of Geometry

Author : Sherman K. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 1470451115
Total Pages : 207 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebra and Tiling: Homorphisms in the Service of Geometry by : Sherman K. Stein

Download or read book Algebra and Tiling: Homorphisms in the Service of Geometry written by Sherman K. Stein and published by American Mathematical Soc.. This book was released on 1993-12-31 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts. The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.

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.

Old and New Unsolved Problems in Plane Geometry and Number Theory

Author : Victor Klee
Publisher : Cambridge University Press
ISBN 13 : 9780883853153
Total Pages : 392 pages
Book Rating : 4.8/5 (531 download)

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Book Synopsis Old and New Unsolved Problems in Plane Geometry and Number Theory by : Victor Klee

Download or read book Old and New Unsolved Problems in Plane Geometry and Number Theory written by Victor Klee and published by Cambridge University Press. This book was released on 1991 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses 24 unsolved problems in number theory and geometry.

The Tiling Book

Author : Colin Adams
Publisher : American Mathematical Society
ISBN 13 : 1470468972
Total Pages : 310 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis The Tiling Book by : Colin Adams

Download or read book The Tiling Book written by Colin Adams and published by American Mathematical Society. This book was released on 2022-08-18 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there is both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

Famous Functions in Number Theory

Author : Bowen Kerins
Publisher : American Mathematical Soc.
ISBN 13 : 147042195X
Total Pages : 203 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Famous Functions in Number Theory by : Bowen Kerins

Download or read book Famous Functions in Number Theory written by Bowen Kerins and published by American Mathematical Soc.. This book was released on 2015-10-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. 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, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

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:

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.