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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.
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.
-~- 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.
Geometry is far more than just shapes and numbers. It governs much of our lives, from architecture and data-mining technology to aerodynamic car design, life-like characters in animated movies, the molecules of food, even our own body chemistry. This title discusses the groundbreaking work of Donald Coxeter, the greatest geometer of his age.
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.
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.
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.
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.
Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets.This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation.Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.