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Inside Rubik’s Cube and Beyond
On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"--A game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France and the Magic Cube or Rubik' s Cube in Great Britain and the USA-has sold more than ten million copies. And they were not merely sold! A highly contagious "twist mania" has been spreading throughout families, offices and waiting rooms. Many classrooms sound as if an army of mice were hard at work behind the desks. What is so fascinating about this cube, which competes with Hungar ian salami and the famous Tokajer wine in the currency-winning export market? For one thing, it is an amazing technical tool. How does it work? Moreover, the contrast between its innocent, innocuous appearance and the hidden difficulty of its solution offers a serious challenge to all puzzle fans, but especially to those mathematicians who are profeSSionally concerned with logical deduction
How to Solve the Rubik's Cube
The Rubik's Cube is the world's best-known puzzle, a magical object that has baffled and fascinated the world for over fifty years. This clearly-illustrated step-by-step guide teaches you a foolproof beginners' method for solving the Cube, plus advanced techniques if you want to learn to solve it in seconds. An Official Guide to cracking the cube!
Adventures in Group Theory
This updated and revised edition of David Joyner’s entertaining “hands-on” tour of group theory and abstract algebra brings life, levity, and practicality to the topics through mathematical toys. Joyner uses permutation puzzles such as the Rubik’s Cube and its variants, the 15 puzzle, the Rainbow Masterball, Merlin’s Machine, the Pyraminx, and the Skewb to explain the basics of introductory algebra and group theory. Subjects covered include the Cayley graphs, symmetries, isomorphisms, wreath products, free groups, and finite fields of group theory, as well as algebraic matrices, combinatorics, and permutations. Featuring strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.
Cubed
'More than just a memoir. A manifesto for a whole way of thinking' Daily Mail 'An idiosyncratic and gripping memoir about his life and the indomitable career of the Cube' Observer 'The rise and enduring power of the world's most popular puzzle toy . . . Cubed is less a memoir than a chronicle of Rubik's evolving relationship with his creation' Financial Times *** As a child, Erno Rubik became obsessed with puzzles of all kinds. To him, they weren't just games - they were challenges that captured his imagination, creativity and perseverance. Rubik's own puzzle went on to be solved by millions worldwide, becoming one of the bestselling toys of all time. In Cubed, he tells us the story of the unexpected and unprecedented rise of the Cube for the very first time - and makes a case for why rediscovering our playfulness and inner curiosity holds the key to creative thinking.
Mechanical Engineers' Handbook, Volume 2
Full coverage of electronics, MEMS, and instrumentation and control in mechanical engineering This second volume of Mechanical Engineers' Handbook covers electronics, MEMS, and instrumentation and control, giving you accessible and in-depth access to the topics you'll encounter in the discipline: computer-aided design, product design for manufacturing and assembly, design optimization, total quality management in mechanical system design, reliability in the mechanical design process for sustainability, life-cycle design, design for remanufacturing processes, signal processing, data acquisition and display systems, and much more. The book provides a quick guide to specialized areas you may en...
Economic Models of Material-Product Chains for Environmental Policy Analysis
A theoretical and empirical contribution to the quest for sustainability and environmental quality. The book examines the physical and economic aspects of flows of materials and products, as well as the policies and strategies designed to reduce the related resource depletion and environmental pollution. The `material-product chain' concept forms a general framework, defined as a system of linked flows of materials and products that support the provision of a certain service. Various economic models of material-product chains are studied, both theoretical and applied, such as static optimisation, dynamic simulation and general equilibrium models. Applications to metals, rain gutters and window frames are described. Audience: Readers in universities, research organizations and policy institutes interested in the environment, economics and government policy.
Solving Guide of the Rubik's Cube Puzzle
Many of us have struggled to learn the Rubik’s Cube in its 40 year history. This all inclusive guide will give you the insight to overcome this frustrating obstacle. This book is desirable for kids and beginners. Its step – by – step guide enables the reader to learn quickly. Algorithms aren’t necessary, but I have included them for those interested. The colourful diagrams are clearly illustrated with a nice image. I illustrate the following three things – 1) The pictures of the original position of the cube. 2) The look of the Cube during the moves made. 3) The pictures of what the Cube should look like after the completed moves. Here, you can also learn techniques, and finger tricks to produce faster solves. I offer tips on finger tricks to help work up your speed. I have provided you with information about other prominent Rubik’s Cube solvers, and their world records. You can also read up on the history of the Rubik’s Cube. Finally, I have informed the learner about other learning methods, and named online sites that offer help, and advice on all Rubik’s Cube related activities.
Combinatorics
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
EU and WTO Law
Examining the impact of free trade rules, this survey aims to help clarify the legal boundaries that exist on product regulation between national law, European Union (EU) law, World Trade Organization (WTO) law, and international environmental law. Public authorities make a consistent effort to regulate trade, acting within the policy space that remains open--both at the national and supranational level--while maintaining environmental protection and sustainable development. In exploring this process, this study brings to light the conflict of interests between free trade rules and product-oriented environmental measures. While environmental law increasingly relies on product regulations as an important policy instrument, supranational economic law--as laid down within the framework of the EU and the WTO--tends to view such regulations as trade barriers, which are to be removed as far as possible. This apparent contradiction between environmental protection and trade liberalization is analyzed closely, revealing why it has been the subject of much political and academic debate.
