Puzzles Involving Polycubes Triangulations And Polyhexes

Author : Raymond R. Fletcher
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 2023-04-26
Category : Mathematics
ISBN : 1959379542

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Puzzles Involving Polycubes, Triangulations and Polyhexes by Raymond R. Fletcher Pdf

Three related types of puzzles are featured in this book. All involve labeling the vertices or edges of graphs. The first type of graph is a polycube. The vertices are labeled with a specific set of numbers and the puzzle involves obtaining a labeling in which the four vertices belonging to each face of a constituent cube have the same sum. The second type of graph is a plane triangulation. The puzzle involves labeling the edges of each constituent triangle so that the sum is the same for each triangle. The third type of graph is a polyhex. For this type of graph the vertices are labeled with integers so that the sum of the six points bounding each hexagon is the same. Problems and research questions are included at the end of each Section, and all puzzle solutions are provided.

Author : Raymond R. Fletcher III
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 2021-09-25
Category : Electronic
ISBN : 1685360939

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Puzzles Involving Polycubes, Triangulations and Polyhexes by Raymond R. Fletcher III Pdf

Author : Raymond R. Fletcher III
Publisher : Xlibris Corporation
Page : 191 pages
File Size : 54,7 Mb
Release : 2024-07-04
Category : Mathematics
ISBN : 9781796030761

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Polycubes, Triangulations and Polyhexes over Zn by Raymond R. Fletcher III Pdf

A mathematical puzzle book that involves labeling points or edges on three types of graphs: (1) polycubes, which consist of cubes attached face-to-face, (2) polyhexes, which consist of regular hexagons joined edge to edge, and (3) triangulations, which consist of triangles attached edge to edge. For a polycube with n points, the puzzle consists of labeling each vertex with the full set of integers (mod n), (Zn) so that the four labels belonging to each face of every component cube have the same sum. For a polyhex with n points, the vertices are to be labeled with elements from Zn so that the six labels assigned to each component hexagon have the same sum. For puzzles involving triangulation, the edges, instead of the vertices, are to be labeled with elements of Zn. To solve the puzzle, a labeling must be found so that the edges of each component triangle have the same sum. Unlike sudoku, these puzzles have many solutions; the solutions provided in the back of the book are included just to show that a solution exists. Readers are encouraged to create and solve their own puzzles in any of the three genres. Questions of mathematical interest are provided throughout.

Author : Raymond R. Fletcher III
Publisher : Xlibris Us
Page : 202 pages
File Size : 48,5 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 : Raymond R. Fletcher III
Publisher : Xlibris Corporation
Page : 245 pages
File Size : 55,9 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 : David A. Klarner
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 49,8 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 : Jin Akiyama,Bo Jiang,Mikio Kano,Xuehou Tan
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 45,7 Mb
Release : 2011-10-26
Category : Computers
ISBN : 9783642249822

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Computational Geometry, Graphs and Applications by Jin Akiyama,Bo Jiang,Mikio Kano,Xuehou Tan Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the China-Japan Joint Conference on Computational Geometry, Graphs and Applications, CGGA 2010, held in Dalian, China, in November 2010. The 23 revised full papers presented were carefully selected during two rounds of reviewing and improvement from numerous submissions. All aspects of computational and discrete geometry, graph theory, graph algorithms, and their applications are covered.

Author : Thomas Snyder,Wei-Hwa Huang
Publisher : Sterling Publishing Company, Inc.
Page : 148 pages
File Size : 49,7 Mb
Release : 2009-09
Category : Games & Activities
ISBN : 1402765029

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Mutant Sudoku by Thomas Snyder,Wei-Hwa Huang Pdf

Run for cover, because Mutant Sudoku is on the loose! Thomas Snyder and Wei-Hwa Huang are both U.S. Sudoku Champions, and they’ll have you filling in grids of all shapes and sizes, testing parts of your logical mind that have never been tested before. You will marvel at the ingenuity within these pages, and after experiencing the power of these Mutant Sudoku, normal 9 x 9 puzzles will never seem the same again.

Author : Siobhan Roberts
Publisher : Unknown
Page : 400 pages
File Size : 53,9 Mb
Release : 2007-07
Category : Geometry
ISBN : 0887847773

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King of Infinite Space by Siobhan Roberts Pdf

In the tradition of A Beautiful Mind, here is an engaging biography of a world-famous Canadian geometry genius, Donald Coxeter, whose work has slowly and steadily become the air we breathe, with everyday applications in telecommunication and e-commerce, among other fields. King of Infinite Space combines two bestselling categories, popular science and biography. It makes geometry accessible through the fascinating life of the 20th century's greatest classical geometer -- a man who also happens to be a Canadian. Coxeter's story weaves together several rich and surprising threads, from the idiosyncratic nature of his personal life to the geopolitical fabric of his times -- what he calls the wild wicked world -- and illuminates the importance of mathematics therein. Indeed, Coxeter is credited with saving classical geometry from near extinction: for over fifty years, he fought a quiet war of attrition against disdain for his unfashionable geometry, stoically retaining his passion for the beauty of shapes.

Author : Martin Gardner
Publisher : W W Norton & Company Incorporated
Page : 494 pages
File Size : 41,5 Mb
Release : 2006
Category : Games & Activities
ISBN : 0393061140

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The Colossal Book of Short Puzzles and Problems by Martin Gardner Pdf

The renowned provocateur of popular math presents a collection of his widely recognized short puzzles--along with a few new ones--that explore chess, physics, probability, and topology, among other topics.

Author : Paul R. Halmos
Publisher : American Mathematical Soc.
Page : 421 pages
File Size : 41,7 Mb
Release : 2020-08-03
Category : Mathematics
ISBN : 9781470459161

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I Want to Be a Mathematician: An Automathography by Paul R. Halmos Pdf

Author : Tony Marolt
Publisher : Page Publishing Inc
Page : 119 pages
File Size : 49,9 Mb
Release : 2022-11-03
Category : Business & Economics
ISBN : 9781642985214

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The Leadership Quotient by Tony Marolt Pdf

You are already a leader, even if you don't yet know it. You can become a great leader, which the world desperately needs - leaders with courage, compassion, and the ability to raise each unique individual to their highest levels of performance. Leadership is a learned series of skills and behaviors; however, the path to becoming a great leader first begins with the acknowledgment that you are one, followed by your strong desire and commitment to be a great one. The leadership quotient is built on the premise and promise that everyone is a leader and that only by increasing the degree of mastery in all four critical areas can an individual transition from ordinary or mediocre into the more aspirational, urgently needed realm of truly great leaders. This practical guide to leadership is filled with tools and real-world examples that you can quickly add to your repertoire and immediately apply within your organization. These tools can be leveraged by every reader, from those who have never led before to those who have been leading for years. The Chinese philosopher Lao-Tzu captured the essence of the leadership quotient principles in his quote, which ends with the line, "But of a good leader, who talks little, when his work is done, his aim fulfilled, they will all say, We did this ourselves." If you aspire to become that kind of leader, to add tools to your belt that position you to lead extremely well, then this book and those tools are your path to achieve that aspiration.

Author : Sara Enochs
Publisher : Unknown
Page : 372 pages
File Size : 55,6 Mb
Release : 2021-01-27
Category : Electronic
ISBN : 1648034799

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The Call to See by Sara Enochs Pdf

Ava Andrews is a mom with big dreams to save life on planet Earth from needless violence, disease, and global warming. Ah! No pressure. All of her life she has listened to her father, Scott Ballantyne, an inventor, paint a picture of a better world where the air is clear, the water is pure, and the soil grows healthy food. Now that her kids are on their way to becoming adults and climate change increasingly threatens all life on Earth, what can she do to protect this world she so dearly loves? As Ava races through time with her daydreaming ways to see the future, can the code she cracked years before to fix everything be applied in time to work? And, more importantly, what can she do now to save life on Earth? Come with Sara Enochs as she explores the many roles associated with being a woman over a lifetime with a cast of characters to analyze what it means to be a daughter, sister, wife, mother, grandmother. As she moves the story forward, through the eyes of these complex and creative but loveable characters, The Call To See, reveals many intricate layers uncovering hidden observations that leaves much to ponder while offering solutions.

Author : John Barnes
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 49,6 Mb
Release : 2012-08-17
Category : Mathematics
ISBN : 9783642309649

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Gems of Geometry by John Barnes Pdf

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Author : Lasse Rempe-Gillen, Rebecca Waldecker
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 44,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780821898833

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Primality Testing for Beginners by Lasse Rempe-Gillen, Rebecca Waldecker Pdf

How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.