Classic Ebooks
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 Over 100 Classic eBooks for Sony Reader all models US $3.99
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 Classic Country Pancake Recipe EBook Mammas Secret US $1.00
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 Cocktail VODKA RUM GIN Classic RecipesExcellent eBooks US $.89
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 ON DVD 10000 Classic PDF EBOOKS US $6.99
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 THE ART OF WAR By Sun Tzu A Classic E book On CD US $.01
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 25000 Classic epub eBooks for Apple iPad on 2 discs US $6.49
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 300 Classic eBooks for Sony Reader PRS on CD lrf US $3.99
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So you think that math does not teach you things like solving Rubik's cube? Then think again. My ability to figure out the 3x3 cube lies not so much in my inherent brilliance but because my mathematical training taught me how to problem solve and to figure out things that without such training, I would never have figured out, or even attempted. Not that the Rubik's cube is as difficult as the Einstein Field Equations, but with 43 quintillion possibilities, it is certainly no walk in the park either. The wonderful field of mathematics helped train me to tackle this world-famous brain buster.
The Rubik's cube is actually a very interesting mathematical object. Its mathematics lies within the realm of group theory and the cube itself is known as a permutation group. Specifically, the cube is a group which is generated by the rotations of its six faces. The size of this group is enormous-to the tune of 43 quintillion (a quintillion is a 1 followed by 18 0's-for more on this, see my article "Numbers - How Big is Big?"), and the set of permutations generated by the cube is governed by typical group properties. Let me explain.
A group is a set of objects that has the property that when you perform the mathematical operation imposed on the group, you end up with another object within the set. The "mathematical operation" associated with the Rubik's cube group is the rotation of its faces. Each of these moves is known as a permutation because we are permuting the color facelets on the cube, but we are still ending up with a cube, albeit in a different arrangement of the color facelets. This group operation of "rotation of the faces of the cube" must also be associative, which in this case it is, since we can take three moves of the cube, call them A,B, and C and associate them as (AB)C or A(BC) and end up with the same ultimate move. Each move has an opposite, or inverse (just reverse the rotation); moreover, though not obvious, the cube has an identity element which will return any position of the cube, or any arrangement of the cube, back to its original position. The existence of these properties impose a group structure on the Rubik's cube.
Now anyone can cheat and learn to solve the cube by studying another's solution. The trick is to solve it using your own solution-that is figuring out the cube. The cube can be very frustrating but what if you were stranded like Tom Hanks in the movie Castaway? Do you think you would figure it out given enough time? Or would you do what most do and quit? What if someone said that in order to get off that tropical island you had to figure it out? Faced with this ultimatum, I can pretty much say that you would come up with some creative problem solving strategies to solve that cube and get off that island. Unless of course, you like coconuts and crab that much.
Now what you would probably do in this situation, after much trial and error, is to find out how to get the cube solved to the top layer. You would get to this point after much practice; after many, many mistakes, false starts, and restarts; and after much head banging. You would then ultimately figure out how to get the remaining 9 facelets into their correct positions and orientations, discovering certain moves which fixed certain cubes and changed others more to your liking.
After much wrangling and brain-sweating, you would come to know the moves that oriented your facelets in exactly the way you needed them when you got to that top layer. In fact, these "orientation moves" are actually permutations which preserve certain positions of the cube while altering others so that the cube can be restored to normal, normal being the solved position, or the one in 43 quintillion!
The point of this article is that you have the power to solve the cube if you put your mind to it. And what a sense of satisfaction you will get when you know you just whipped into shape a permutation group of size 43 quintillion! So try the cube and remember: you can solve it if you only try. I did it and so can you.
See a list of my ebooks here at Order Ebooks
Joe is a prolific writer of self-help and educational material and an award-winning former teacher of both college and high school mathematics. Joe is the creator of the Wiz Kid series of math ebooks, Arithmetic Magic, the little classic on the ABC's of arithmetic, the original collection of poetry, Poems for the Mathematically Insecure, and the short but highly effective fraction troubleshooter Fractions for the Faint of Heart. The diverse genre of his writings (novel, short story, essay, script, and poetry)-particularly in regard to its educational flavor- continues to captivate readers and to earn him recognition.
Joe propagates his teaching philosophy through his articles and books and is dedicated to helping educate children living in impoverished countries. Toward this end, he donates a portion of the proceeds from the sale of every ebook. For more information go to http://www.mathbyjoe.com
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Amazon Kindle 2 / Kindle 2 International E-Book Reader Classic Water Resistant Messenger Bag with Tuck-Away Fanny Straps - black List Price: $89.99 Sale Price: $14.61  |
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The Classic Water Resistant Messenger Bag with Tuck-Away Fanny Strap provides perfect protection for your Kindle. It features 15 multi-functional pockets with spacious main compartment, mp3 player pocket with earphone port, cellphone pocket, etc... |
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Sumdex Classic Metrobrief Lite Computer Notebook Bag List Price: $59.95 Sale Price: $25.38 |
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The Metrobrief Lite by Sumdex is a stylish, compact, and lightweight brief made to fit most 14.1" screen sized laptops. The front panel features a multi-function workstation and a handy zippered compartment for the laptop's AC adapter and other peripherals. |
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Classic Straight USB Cable for the HanLin eBook V5 with Power Hot Sync and Charge capabilities - uses Gomadic TipExchange Technology List Price: $27.95 Sale Price: $17.95 |
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Charge your mobile devices while synchronizing data with one cable custom designed to work with our TipExchange Technology that enables hundreds of mobile devices to work with the same cable (Tip Included)... |
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JAVOedge Classic Leather Book Case for the Barnes & Noble Nook List Price: $49.95 Sale Price: $39.95 |
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For classic, professional appeal, JAVOedge's Classic Leather Book Case for the Barnes & Nobles Nook carries your eReader in stylish protection. Made of premium soft leather, the Nook Classic Flip Case offers full front, side, and back protection to your eReader against bumps, drops, scratches... |
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JAVOedge Classic Leather Case for the Sony Reader 300 List Price: $49.95 Sale Price: $10.95 |
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Protect your Sony Reader 300 in a stylish, protective case from JAVOedge. The JAVOedge Classic Leather Case is a Classy and traditional leather cases which prtects your device in style. Featuring a book-style jacket, the cases design offers a snug, padded fit for your Sony Reader... |
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Ebooks $14.95 Ebooks |
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An Empirical Design for Ebooks $14.65 An Empirical Design for Ebooks |
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An Empirical Design For Ebooks $10.68 Buy and sell [An Empirical Design For Ebooks] at great prices. |
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An Empirical Design for eBooks $17.98 An Empirical Design for eBooks by Harold, and Ph.D. Henke Published in 2003 by Chartula Press |
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Self-Publishing Ebooks And Pods $9.33 Buy and sell [Self-Publishing Ebooks And Pods] at great prices. |
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How To Become Wealthy Selling Ebooks On The Internet $15.24 Buy and sell [How To Become Wealthy Selling Ebooks On The Internet] at great prices. |
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An Empirical Design for eBooks $14.89 This book is in Good Used condition |
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Self-Publishing Ebooks and Pods: One Step at a Time - Second Edition $12.73 Self-Publishing Ebooks and Pods: One Step at a Time - Second Edition |
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Learn How to Become Wealthy Selling eBooks $23.98 Did you know...? Stephen King brought epublishing to the attention of the world by publishing his novel, Riding the Bullet, exclusively in ebook form. In the first 24 hours of availability, 400,000 copies were downloaded - more than any other book in any format! Epublishing is becoming today''s future. Learn How to Become Wealthy Selling Ebooks helps individuals become wealthy at creating and selling ebooks. This book is necessary for any perspective ebook entrepreneur. Using the techniques in this book, you will learn how to create your own ebook money tree. In the past, prospective authors had to hope that a publisher would pick up their book and have their work put into print. Today, an informed author can take control of their publishing needs and publish their work themselves. Using this book and the information will help you create, sell, market, and profit from ebooks. This book will help you create strategies to sell ebooks and become a success at it. |
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Ebooks: Idea to Amazon in 14 Days $14.58 No Synopsis Available |
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MLC Junior eTextbook Bundle (EBOOKS ONLY) $283.68 No Synopsis Available |
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MLC Senior eTextbook Bundle (EBOOKS ONLY) $181.68 No Synopsis Available |
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MLC Sophomore eTextbook Bundle (EBOOKS ONLY) $559.44 No Synopsis Available |
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MLC Sophomore eTextbook Bundle (EBOOKS ONLY) $559.44 No Synopsis Available |
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MLC Senior eTextbook Bundle (EBOOKS ONLY) $181.68 No Synopsis Available |
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MLC Junior eTextbook Bundle (EBOOKS ONLY) $283.68 No Synopsis Available |
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How to Become Wealthy Selling Ebooks on the Internet $24.33 No Synopsis Available |
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Make Money Online-Write and Sell eBooks Guide: A Work from Home Internet Business Writing, Selling eBooks Online $27.63 The ultimate guide to starting and running an online business walks readers through every single detail from choosing a profitable niche market to writing or outsourcing an e-book to marketing to millions in electronic and print formats. |
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ePub Straight to the Point: Creating ebooks for the Apple iPad and other ereaders $18.33 No Synopsis Available |
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How to Make, Market and Sell Ebooks - All for Free: Ebooksuccess4free $9.74 No Synopsis Available |
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The classic $65 The classic |
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The classic $60 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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The classic $65 The classic |
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Classic $3.93 Classic |
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Classic $3.93 Classic |
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Classic $3.93 Classic |