Polyominoes: A Guide to Puzzles and Problems in Tiling

Polyominoes: A Guide to Puzzles and Problems in Tiling
Author: George E. Martin
Publisher: American Mathematical Soc.
Total Pages: 199
Release: 2020-08-03
Genre: Mathematics
ISBN: 1470457342

Polyominoes will delight not only students and teachers of mathematics at all levels, but will be appreciated by anyone who likes a good geometric challenge. There are no prerequisites. If you like jigsaw puzzles, or if you hate jigsaw puzzles but have ever wondered about the pattern of some floor tiling, there is much here to interest you. A polyomino is a shape cut along the lines from square graph paper; the pronunciation of polyomino begins as does polygon and ends as does domino. Tilings, also called tessellations of mosaic patterns, are older than civilization itself. Tiling with polyominoes provides challenges that range from the popular jigsaw-like puzzles to easily understood mathematical research problems. You will find unsolved puzzles and problems of both kinds here. Answers are provided for most of the problems that have known solutions. It is only fair to repeat here the warning stated in the preface to this book, "Playing with polyominoes can be habit forming."

Polyominoes

Polyominoes
Author: Solomon W. Golomb
Publisher: Princeton University Press
Total Pages: 204
Release: 2020-06-30
Genre: Mathematics
ISBN: 0691215057

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.

Polyominoes

Polyominoes
Author: George Martin
Publisher: Cambridge University Press
Total Pages: 200
Release: 1991
Genre: Mathematics
ISBN: 9780883855010

A book for anyone who likes a good geometric challenge.

Polygons, Polyominoes and Polycubes

Polygons, Polyominoes and Polycubes
Author: A. J. Guttmann
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2009-05-18
Genre: Science
ISBN: 1402099266

The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.

Homage to a Pied Puzzler

Homage to a Pied Puzzler
Author: Alan Schoen
Publisher: CRC Press
Total Pages: 320
Release: 2009-02-26
Genre: Mathematics
ISBN: 1439865000

The tradition of honoring Martin Gardner continues with this edited collection of articles by those who have been inspired by Gardner to enter mathematics, to enter magic, to bring magic into their mathematics, or to bring mathematics into their magic. Contributing authors include world-leading puzzle designers, puzzle collectors, mathematicians, a

Real-World Algorithms

Real-World Algorithms
Author: Panos Louridas
Publisher: MIT Press
Total Pages: 527
Release: 2017-03-17
Genre: Computers
ISBN: 0262035707

An introduction to algorithms for readers with no background in advanced mathematics or computer science, emphasizing examples and real-world problems. Algorithms are what we do in order not to have to do something. Algorithms consist of instructions to carry out tasks—usually dull, repetitive ones. Starting from simple building blocks, computer algorithms enable machines to recognize and produce speech, translate texts, categorize and summarize documents, describe images, and predict the weather. A task that would take hours can be completed in virtually no time by using a few lines of code in a modern scripting program. This book offers an introduction to algorithms through the real-world problems they solve. The algorithms are presented in pseudocode and can readily be implemented in a computer language. The book presents algorithms simply and accessibly, without overwhelming readers or insulting their intelligence. Readers should be comfortable with mathematical fundamentals and have a basic understanding of how computers work; all other necessary concepts are explained in the text. After presenting background in pseudocode conventions, basic terminology, and data structures, chapters cover compression, cryptography, graphs, searching and sorting, hashing, classification, strings, and chance. Each chapter describes real problems and then presents algorithms to solve them. Examples illustrate the wide range of applications, including shortest paths as a solution to paragraph line breaks, strongest paths in elections systems, hashes for song recognition, voting power Monte Carlo methods, and entropy for machine learning. Real-World Algorithms can be used by students in disciplines from economics to applied sciences. Computer science majors can read it before using a more technical text.

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries
Author: Paulus Gerdes
Publisher: Lulu.com
Total Pages: 204
Release: 2008-06-26
Genre: Art
ISBN: 1435726294

The book "Lunda Geometry" explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author's research of 'sona', illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.Several chapters were published in journals like 'Computers & Graphics' (Oxford), 'Visual Mathematics' (Belgrade), and 'Mathematics in School' (UK).

Hexaflexagons and Other Mathematical Diversions

Hexaflexagons and Other Mathematical Diversions
Author: Martin Gardner
Publisher: American Mathematical Soc.
Total Pages: 200
Release: 2020-10-05
Genre: Mathematics
ISBN: 1470463520

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 volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.

Pentomino Puzzles

Pentomino Puzzles
Author: Eric Harshbarger
Publisher: Puzzlewright
Total Pages: 0
Release: 2011
Genre:
ISBN: 9781402766992

Pentominoes drive puzzle fans wild-and a complete set of these versatile tiles is packaged with every copy of this fun-filled book! These 12 unique shapes, each formed by 5 squares joined edge to edge, must be fitted together to match specific patterns-from simple rectangles to animals and people. Eric Harshbarger is a mathematician by education, a computer engineer by trade, and a puzzle wizard by personal choice. His website (www.ericharshbarger.org) features his astounding creations with Lego bricks, among other marvels. Book comes with a full set of plastic pentominoes, making this a great gift

Graph Theory and Computing

Graph Theory and Computing
Author: Ronald C. Read
Publisher: Academic Press
Total Pages: 344
Release: 2014-05-12
Genre: Mathematics
ISBN: 1483263126

Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.