Polyparallelogram Puzzles And Tiling Problems

Author : Raymond R. Fletcher III
Publisher : Xlibris Corporation
Page : 245 pages
File Size : 43,5 Mb
Release : 2024-07-04
Category : Mathematics
ISBN : 9781796097894

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Polyparallelogram Puzzles and Tiling Problems by Raymond R. Fletcher III Pdf

A mathematical puzzle book which involves labeling vertices of a plane graph with elements from an abelian group G such that the labels applied to the bounding vertices of each region have the same sum in G. The plane graphs are those formed by the edges and vertices of various types of parallelograms fitted together edge to edge. We call these polyparallelograms. The polyparallelogram puzzles are organized into the following categories according to the types of parallelograms involved: (i) polysquares (or polyominoes; (ii) 60/120 rhombs; (iii) 36/144 and 72/108 rhombs (Penrose rhombs); (iv) various lattice parallelograms. The reader is introduced to the theory of polyparallelogram tilings of polygons, and challenged with problems and research questions at the end of each Chapter. All that is required of the elementary theory of graphs and abelian groups is included in the text. Also included are a variety of pure tiling problems involving nonparallelogram lattice quadrilaterals. “Polyparallelogram Puzzles and Tiling Problems” is a sequel to “Polycubes, Triangulations and Polyhexes over Zn” and features a similar type of puzzle but is more engaging mathematically.

Author : Raymond R. Fletcher III
Publisher : Xlibris Us
Page : 202 pages
File Size : 50,9 Mb
Release : 2020-04-24
Category : Mathematics
ISBN : 179609790X

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Polyparallelogram Puzzles and Tiling Problems by Raymond R. Fletcher III Pdf

A mathematical puzzle book which involves labeling vertices of a plane graph with elements from an abelian group G such that the labels applied to the bounding vertices of each region have the same sum in G. The plane graphs are those formed by the edges and vertices of various types of parallelograms fitted together edge to edge. We call these polyparallelograms. The polyparallelogram puzzles are organized into the following categories according to the types of parallelograms involved: (i) polysquares (or polyominoes; (ii) 60/120 rhombs; (iii) 36/144 and 72/108 rhombs (Penrose rhombs); (iv) various lattice parallelograms. The reader is introduced to the theory of polyparallelogram tilings of polygons, and challenged with problems and research questions at the end of each Chapter. All that is required of the elementary theory of graphs and abelian groups is included in the text. Also included are a variety of pure tiling problems involving nonparallelogram lattice quadrilaterals. "Polyparallelogram Puzzles and Tiling Problems" is a sequel to "Polycubes, Triangulations and Polyhexes over Zn" and features a similar type of puzzle but is more engaging mathematically.

Author : George Martin
Publisher : Cambridge University Press
Page : 200 pages
File Size : 44,8 Mb
Release : 1991
Category : Mathematics
ISBN : 0883855011

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Polyominoes by George Martin Pdf

A book for anyone who likes a good geometric challenge.

Author : Francesco D'Andrea
Publisher : Springer Nature
Page : 203 pages
File Size : 40,9 Mb
Release : 2023-08-19
Category : Mathematics
ISBN : 9783031284281

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A Guide to Penrose Tilings by Francesco D'Andrea Pdf

This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.

Author : Anonim
Publisher : Unknown
Page : 968 pages
File Size : 51,6 Mb
Release : 1975
Category : Science
ISBN : UOM:39015010895251

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Scientific American by Anonim Pdf

Author : George Pólya
Publisher : Princeton University Press
Page : 288 pages
File Size : 48,5 Mb
Release : 2014
Category : Mathematics
ISBN : 9780691164076

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How to Solve it by George Pólya Pdf

"Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams."--Back cover.

Author : Paul Zeitz
Publisher : John Wiley & Sons
Page : 389 pages
File Size : 45,8 Mb
Release : 2017
Category : Problem solving
ISBN : 9781119239901

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The Art and Craft of Problem Solving by Paul Zeitz Pdf

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

Author : Peter Brass,William O. J. Moser,János Pach
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 50,7 Mb
Release : 2006-06-19
Category : Mathematics
ISBN : 9780387238159

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Research Problems in Discrete Geometry by Peter Brass,William O. J. Moser,János Pach Pdf

This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Author : Solomon W. Golomb
Publisher : Princeton University Press
Page : 204 pages
File Size : 50,5 Mb
Release : 2020-06-30
Category : Mathematics
ISBN : 9780691215051

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Polyominoes by Solomon W. Golomb Pdf

Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.

Author : Martin Gardner
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 50,5 Mb
Release : 2020-10-06
Category : Mathematics
ISBN : 9781470463656

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Time Travel and Other Mathematical Bewilderments by Martin Gardner Pdf

Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This is the original 1988 edition and contains columns published from 1974-1976.

Author : Arthur Engel
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 50,5 Mb
Release : 2008-01-19
Category : Mathematics
ISBN : 9780387226415

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Problem-Solving Strategies by Arthur Engel Pdf

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 40,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853689

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Mostly Surfaces by Richard Evan Schwartz Pdf

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

Author : David A. Klarner
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468466867

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The Mathematical Gardner by David A. Klarner Pdf

-~- T he articles in this book are dedicated to Martin Gardner, the world's greatest expositor and popularizer of mathematics. While our papers are confined to this single subject, Gardner's interests and accomplishments have a wide range of subjects. Hence, we have entitled the book the Mathematical Gardner, and would like to see other volumes such as the Magical, the Literary, the Philosophical, or the Scientific Gardner accompany it. Of course, our title is also an appropriate pun, for Martin Gardner's relationship to the mathematical community is similar to a gardener's relationship to a beautiful flower garden. The contributors to this volume comprise only a small part of a large body of mathematicians whose work has been nurtured by its exposition in "Mathematical Games"; Martin's column which appears every month in Scientific American. More than just a mathematical journalist, Martin connects his readers by passing along problems and information and stimulating creative activity. Thus, he is a force behind the scenes as well as a public figure. Two people were particularly helpful in putting this book together.

Author : Percy Alexander MacMahon
Publisher : Unknown
Page : 136 pages
File Size : 40,9 Mb
Release : 1921
Category : Mathematical recreations
ISBN : WISC:89041209628

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New Mathematical Pastimes by Percy Alexander MacMahon Pdf

Author : Dušan Djukić,Vladimir Janković,Ivan Matić,Nikola Petrović
Publisher : Springer Science & Business Media
Page : 819 pages
File Size : 51,8 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9781441998545

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The IMO Compendium by Dušan Djukić,Vladimir Janković,Ivan Matić,Nikola Petrović Pdf

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.