## Nov 23, 2009

### Tribotix - Articles & Tutorials: Mathematics and Technical HowTo in Robotics

http://www.tribotix.info/Articles&Tutorials/ArticlesTutorials.htm

# Articles & Tutorials ....

## Articles

 Adding Bluetooth to the CM5 module Adding Bluetooth to the CM5 module This article describes in detail how you can add an ESD200 to the CM5 module. The article shows 2 ways this can be achieved: for CM5 to CM5 communication, or for CM5 to PC communication Mathematics required for Robotic Motion Mathematics required for Robotic Motion This articles describes in detail the mathematics involved in Inverse Kinematics. The article presents full solutions for both Algebraic and Geographical solutions. The article then goes on to apply the Inverse Kinematic solutions to show how a 2DOF robotic limb can track an elliptical trajectory.

## Tutorials

 Date Created Description 20/07/06 Robotis Updating AX-12 firmware 10/08/08 RoboBuilder How to Change wCK ID 10/08/08 RoboBuilder How to replace wCK gears 10/08/08 RoboBuilder How to fit Accelerometer module 10/08/08 RoboBuilder Motion Builder Tutorial 10/08/08 RoboBuilder Programming the RBC in C 10/08/08 RoboBuilder RBC GPIO allocation 10/08/08 RoboBuilder wCK Communication Protocol 10/08/08 RoboBuilder IR Remote Control Commands

### Magic Circles

http://www.cgl.uwaterloo.ca/~smann/Magic/index.html

# Magic Circles

Last Updated: September 16, 2002
This page contains some work I've done on magic circles. Most of the work on these pages was either inspired by (or directly from) Clifford Pickover's book (The Zen of Magic Squares, Circles and Stars) or by W.S. Andrews's book (Magic Squares and Cubes, available at Amazon.com). A magic circle is actually a set of circles, where integers are placed at the intersections of two circles. The set of circles and integers is said to be magic if the integers on each circle sum to the same value.

Here is a simple example of a magic circle:

The numbers on each of the three circles sum to 14.

## Related Pages

The following is hardly an exhaustive list.

Stephen Mann
smann@uwaterloo.ca
University of Waterloo | School of Computer Science | 200 University Ave. W. | Waterloo, Ontario Canada | N2L 3G1 | 519.888.4567 | http://www.cgl.uwaterloo.ca/~smann/

## Nov 22, 2009

### The Zen of Magic Squares, Circles, and Stars:

http://sprott.physics.wisc.edu/pickover/math-book.html
http://www.pickover.com/

"Pickover contemplates realms beyond our known reality."
-- The New York Times

"Pickover inspires a new generation of da Vincis to build unknown flying machines and create new Mona Lisas."
-- Christian Science Monitor

"Pickover has published nearly a book a year in which he stretches the limits of computers, art, and thought."
-- Los Angeles Times

"Pickover just seems to exist in more dimensions than the rest of us."
-- Ian Stewart, Scientific American

"Add two doses of Isaac Asimov, and one dose each of Martin Gardner and Carl Sagan, and you get Clifford Pickover, one of the most entertaining and thought provoking writers of our time." -- Michael Shermer, Editor-in-Chief of Skeptic

"Clifford A. Pickover is the heir apparent to Carl Sagan..." -- Robert J. Sawyer, author of Calculating God

"In recent years, Pickover has taken up the helm once worn by Isaac Asimov as the most compelling popular explainer of cutting-edge scientific ideas." -- In Pittsburgh

"Jews in Hyperspace: It's Mel Brooks meets Michio Kaku!" -- Mac Tonnies, author of After the Martian Apocalypse

"A Jewish Da Vinci Code" -- Mariana Tomas, entrepreneur

http://www.cgl.uwaterloo.ca/~smann/Magic/callicrates.html

# The Zen of Magic Squares, Circles, and Stars:

## An Exhibition of Surprising Structures Across Dimensions

### Clifford A. Pickover

Princeton University Press, 2002

 "A refreshing new look at a timeless topic, brimming over with ideas, littered with surprising twists. Anyone who loves numbers, anyone who enjoys puzzles, will find The Zen of Magic Squares, Circles, and Stars compulsive (and compulsory!) reading." - Ian Stewart, University of Warwick   Order from Amazon.com.

• "At first glance magic squares may seem frivolous (Ben Franklin's opinion, even as he spent countless hours studying them!), but I think that is wrong. The great nineteenth-century German mathematician Leopold Kronecker said 'God Himself made the whole numbers--everything else is the work of men,' and Cliff Pickover's stimulating book hints strongly at the possibility that God may have done more with the integers than just create them. I don't believe in magic in the physical world, but magic squares come as close as we will probably ever see to being mathematical magic."
- Paul J. Nahin, University of New Hampshire, author of Duelling Idiots and Other Probability Puzzlers

• "Clifford Pickover has compiled such a wonderfully voluminous collection of magic squares and related configurations that the physical book itself threatens to take the shape of a magic cube. Whether or not you achieve arithmetical satori contemplating these engagingly intricate patterns, you will surely come to appreciate their history, beauty, and richness."
- John Allen Paulos, Temple University, author of Innumeracy and A Mathematician Reads the Newspaper

• "Who would have thought that the simple numbers we used when learning to count as children could be arranged into so many geometric patterns with interesting properties? If playing with numbers is your thing, this latest work by Cliff Pickover will provide you will countless hours of mystical entertainment and mental challenges."
- Julien Clinton Sprott, University of Wisconsin-Madison

• "Pickover carries the mystique of magic squares and their relatives into the twenty-first century with his new book, The Zen of Magic Squares, Circles, and Stars. Whether you're seeking an introduction to magic squares, an in-depth study, some historical information, or just some enjoyable magic figure problems, tricks, properties, or novelties-this book is for you. Pickover does not leave a magic square unturned, and tantalizes us just enough to want to explore further. From the very famous to the less known, Pickover brings them all together in this amazing collection as he points out their roles in science, our lives and the universe."
- Theoni Pappas author of The Joy of Mathematics and Math-A-Day

• "Every generation seems to demand its own updated book dedicated to magic squares. Pickover's work meets the needs of the present generation. It is an enthusiastic, whimsical, and idiosyncratic compendium of magic squares and their variants, some of which are centuries old, some as fresh as corn picked this morning."
- Sherman Stein, University of California, Davis

• "Well documented and illustrated, this book is essentially a huge catalogue of these arithmetical beasts called magic squares. No book that I know of presents such a large range of 'mysterious, odd, and fun' patterns, as the author puts it. This includes the numerous geometrical diagrams that reveal some hidden symmetries not obvious to the eye contemplating the number arrays. Throughout, Pickover convincingly substantiates his claim that the field of magic square study is still wide open."
- Arturo Sangalli, author of The Importance of Being Fuzzy

• "Pickover inspires a new generation of da Vincis to build unknown flying machines and create new Mona Lisas."
- Christian Science Monitor
• "Pickover has published nearly a book a year in which he stretches the limits of computers, art, and thought."
- Los Angeles Times "Bucky Fuller thought big, Arthur C. Clarke thinks big, but Cliff Pickover outdoes them both."
- WIRED
• "Pickover just seems to exist in more dimensions than the rest of us."
- Ian Stewart, author of Does God Play Dice?
• "Strange and beuatiful, stunningly realistic."
- Scientific American
• "Pickover is van Leeuwenhoek's 20th century equivalent."
- OMNI
• "Clifford Pickover is many things -- scientist, scholar, author, editor, and visionary..." - GAMES

 Jacket Flap: Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ''Yu'' square, went on to a life of courtly comfort and fame. (Continued below)

Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization?

Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

See Pickover books at Amazon.Com in separate window.

Introduction and History
1 Construction
2 Classification
3 Gallery 1: Squares, Cubes, and Tesseracts
4 Gallery 2: Circles, and Spheres
5 Gallery 3: Stars and Other Beauties
Some Final Thoughts
Notes

Clifford A. Pickover is the author of over twenty highly-acclaimed books, such as Time: A Traveler's Guide and Computers, Pattern, Chaos, and Beauty, and has written on diverse topics ranging from computers and creativity, art, mathematics, and astronomy-to human behavior and intelligence, time travel, alien life, and science fiction. Dr. Pickover received his Ph.D. from Yale University and is a prolific inventor. His web site pickover.com has received over a half-million visits.

A note on pentamagic squares. As described in my book, a magic square is p-MULTIMAGIC if the square formed by replacing each element by its kth power (for k=1, 2, ?, p) is also magic. (If this definition seems unclear, the book give numerous examples for you to study.) Bimagic squares (2-multimagic) are presented in the book, and references for trimagic squares (3-multimagic) are given. The new multimagic record is a pentamagic square (5-multimagic) built in 2001 by André Viricel and Christian Boyer. Look at Pentamagic, where you can study and download this pentamagic square. This website is in English, French and German.

Return to Cliff Pickover's home page which includes computer art, educational puzzles, higher dimensions, fractals, virtual caverns, JAVA/VRML, alien creatures, black hole artwork, and animations.

## Nov 17, 2009

1. ### YouTube - The Hard Problem: Illusions (2/3)

17 Oct 2009 ... Hard Problems - Older Version. 9826 views. HardProblems · David Albert, Ph.D ON Quantum Physics 1 of 3 · Added to. Quicklist ...
2. ### YouTube - harkerschool's Channel

Trailer for the film Hard Problems: The Road to the World's Toughest Math ... Hard Problems Trailer - Updated. 3:47 January 22, 2008. Film & Animation ...
3. ### YouTube - Interview with Yimin Ge

Hard Problems Trailer - Updated · Added to. Quicklist · 3:47 · Hard Problems Trailer - Updated. 6744 views ... Hard Problems - Older Version. 9826 views ...
4. ### Video results for site:youtube.com "hard problems"

 Hard Problems Trailer - Updated 3 min 47 sec - 22 Jan 2008 www.youtube.com
 Hard Problems - Older Version 3 min 42 sec - 11 Oct 2007 www.youtube.com
 Using Data to "Brute Force" Hard Problems in ... 60 min - 8 Oct 2007 www.youtube.com
 sterotypical Anime Ep5: Simple solutions to ... 24 sec - 11 Jul 2007 www.youtube.com
 YouTube - Algebra Factoring SAT Math Problem ... 4 min 33 sec - 20 Jun 2006 www.youtube.com
 Solving the 2006 IMO Problems: Day 2 10 min - 20 May 2008 www.youtube.com
 YouTube - extremly hard math problem (interactive) 1 min 35 sec - 30 Sep 2008 www.youtube.com
 YouTube - The Hard Problem: Illusions (1/3) 9 min - 26 Sep 2007 www.youtube.com
 YouTube - Math problems for 5 - 8 graders ... 2 min 35 sec - 18 Feb 2008 www.youtube.com
 Gravity Brawl 2009 - highlights 7 min - 8 Jun 2009 www.youtube.com
 YouTube - Math Documentary: Part One 3 min 51 sec - 24 Sep 2007 www.youtube.com
 YouTube - Portugal - 49th International ... 20 sec - 10 Sep 2008 www.youtube.com
 Hard buldring i Norge 2003 9 min - 18 Mar 2008 www.youtube.com
 YouTube - Hard Problem of Consciousness 10 min - 14 Feb 2009 www.youtube.com
 YouTube - Julia Robinson and Hilbert's Tenth ... 6 min - 13 Nov 2007 www.youtube.com
 YouTube - Duke University Math Team Aces ... 3 min 2 sec - 24 Apr 2007 www.youtube.com
 YouTube - Problems We Solve-Understanding "Normal" 2 min 25 sec - 30 May 2008 www.youtube.com
 YouTube - Large image databases and small ... 61 min - 15 May 2008 www.youtube.com
 YouTube - High Fidelity Image-Based Modeling 53 min - 8 Oct 2007 www.youtube.com
 YouTube - Picture taking at the closing ... 58 sec - 7 Aug 2007 www.youtube.com
 YouTube - The Hard Problem: Rivers of Energy (2/3) 9 min - 15 Dec 2007 www.youtube.com
 YouTube - The Hard Problem: Rivers of Energy (1/3) 9 min - 15 Dec 2007 www.youtube.com
 YouTube - IMOers playing Quake3 43 sec - 25 Jul 2007 www.youtube.com
 YouTube - Tim O'Reilly at Web 2.0 expo in San ... 4 min 32 sec - 23 Apr 2008 www.youtube.com
 YouTube - Beautiful Young Minds - Cong's Quote 22 sec - 16 Oct 2007 www.youtube.com
 YouTube - Difficult Functions Question from ... 11 min - 1 Sep 2007 www.youtube.com
 YouTube - Lecture 14 | Convex Optimization II ... 73 min - 9 Jul 2008 www.youtube.com
 YouTube - IMO IRAN 2003 Selection 8 min - 8 Dec 2007 www.youtube.com
 YouTube - 1980 AHSME #14 - Functions 9 min - 1 Sep 2007 www.youtube.com
 YouTube - Science Horizons: Infant Vision ... 60 min - 31 Jan 2008 www.youtube.com
 YouTube - MIT Integration Bee Final Round 1 min 25 sec - 31 Jan 2009 www.youtube.com
 YouTube - Don't Confuse Potential and Actual ... 7 min - 24 Feb 2008 www.youtube.com
 YouTube - IMO 2008 opening ceremony 4 min 53 sec - 27 Oct 2008 www.youtube.com
 YouTube - DAVE GAHAN - SAW SOMETHING 5 min - 18 Nov 2007 www.youtube.com
 YouTube - Lecture 8 | Convex Optimization II ... 71 min - 9 Jul 2008 www.youtube.com
 YouTube - Rock 'n Roll in Math Olympiad 2009 3 min 1 sec - 16 Feb 2009 www.youtube.com
 YouTube - IMO 2007 Closing Ceremony - part 1/3 47 sec - 24 Apr 2008 www.youtube.com
 YouTube - Dinner in Mathematics Camp 1 min 7 sec - 23 Apr 2008 www.youtube.com
 YouTube - hangglider lesson (2006-06-18 part19) 12 sec - 18 Jun 2006 www.youtube.com
 YouTube - The Scala Experiment: Better ... 63 min - 8 Oct 2007 www.youtube.com
 YouTube - Interview with Pascual 6 min - 8 Aug 2007 www.youtube.com
 YouTube - Lecture 17 | Convex Optimization II ... 77 min - 9 Jul 2008 www.youtube.com
 YouTube - Chemistry Olympics 2008 9 min - 28 Feb 2008 www.youtube.com
 YouTube - Hand Math Competition 1 min 15 sec - 22 Aug 2008 www.youtube.com
 YouTube - UKCAT Preparation Abstract Reasoning 2 min 53 sec - 10 Nov 2008 www.youtube.com
 YouTube - Lecture 12 | Convex Optimization II ... 73 min - 9 Jul 2008 www.youtube.com
 YouTube - Lecture 6 | Convex Optimization II ... 72 min - 9 Jul 2008 www.youtube.com
 YouTube - Lecture 3 | Convex Optimization II ... 75 min - 9 Jul 2008 www.youtube.com
 YouTube - SAIC Tsunami Buoy TV Commercial 32 sec - 1 Oct 2008 www.youtube.com
 YouTube - IMC 2008 MATH COMPETITION 3 min 29 sec - 1 Nov 2008 www.youtube.com
5. ### YouTube - A grade four pupil from Oton is a math wizard

Related Videos. Hard Problems Trailer - Updated ... Hard Problems - Older Version. 10060 views. HardProblems · Mental Math Competition Finals Part 2 ...
6. ### YouTube - FAMILY GUY DRAWINGS!!

FAMILY GUY DRAWINGS!!..these are old drawings i did for my avanced algebra and trig class. man those were hard problems..i think i got an A..these were ...
7. ### YouTube - JediHardSkull's Channel

Well, i'm having hard problems in my real life, so, i can't do many videos, but, when i solve my problems, i'll make more videos, ok? ...
8. ### YouTube - 2009 My year so far

13 Sep 2009 ... My year so far, its been full alot of hard problems i lost a friend who is in heaven and ive lost a lover who now also in heaven. my friends ...
9. ### YouTube - "The World's Problems" 10-21-07 PM (Part 1)

3:41. Hard Problems - Older Version. 8722 views. HardProblems · Northern Arizona University: Solving the World's Problems ...
10. ### YouTube - ramkumarkoppu's Channel

Solving hard problems is where you will get the biggest leverage. Tip 5: Don't pay attention to the VC bandwagon. Don't start a company just because you can ...
11. ### YouTube - Constructing a Cube

11 Nov 2009 ... Hard Problems - Older Version. 10099 views ... Hard Problems Trailer - Updated. 6972 views. HardProblems. Loading... See all 1957 videos ...
12. ### YouTube - I Want to Be a Mathematician: A conversation with Paul ...

Hard Problems - Older Version · Added to. Quicklist · 3:42 · Hard Problems - Older Version. 9872 views. HardProblems · A Mathematician's Apology - Review ...

14. ### YouTube - cij81670's Channel

2009 was not a disapointement with big names, hard problems and crazy lighting. music : "Fake Gold" and "Other Girls" by Tigercity - www.myspace.com/ ...
15. ### YouTube - Bouldering: Lynxklippan, Värmdö (TimeLapse 090515)

14 Jun 2009 ... A quick morning boulder at Lynxklippan (http://sverigeforaren.se/index.php/Lynxklippan).To hard problems
but the coffee was great!
16. ### YouTube - Neil Gresham - Guest Setter May 2008

With one eye on creating a unique training facility and the other on producing fiercly hard problems. Neil has aslo recreated several Font classics ...
17. ### YouTube - MathFest Competition Founded By Dr. Ron Boykins

24 Aug 2009 ... Hard Problems Trailer - Updated · Added. 3:47. Hard Problems Trailer - Updated. 5882 views ... Hard Problems - Older Version. 9205 views ...
18. ### YouTube - Maths By Max Double Speed

Hard Problems Trailer - Updated · Added to. Quicklist · 3:47 · Hard Problems Trailer - Updated. 6431 views ... Hard Problems - Older Version. 9579 views ...
19. ### YouTube - Anberlin :: Haight St Cover

Hard Problems Trailer - Updated. 6870 views. HardProblems · Joe satriani - Down down down (cover) · Added to. Quicklist ...
20. ### YouTube - algebra exponents quotient rule x to the eighth

Frankly speaking, hard problems require better problem solvers. Sample list of problems: Rational discourse with fellow human beings: logic and math ...
21. ### YouTube - algebra rule variable in the exponent (4x^2y)^2

10 Jun 2009 ... Frankly speaking, hard problems require better problem solvers. Sample list of problems: Rational discourse with fellow human beings: logic ...
22. ### YouTube - Interview with Peter Scholze

Related Videos. Hard Problems - Older Version · Added to. Quicklist · 3:42 · Hard Problems - Older Version. 9910 views ...
23. ### YouTube - runthemdownonme's Channel

[TRANSLATED] SEXY CHUBBY NURSE TAKING CARE OF ALL MY HARD PROBLEMS. SEXY CHUBBY NURSE TAKING CARE OF ALL MY HARD PROBLEMS Want Free BBW Video Downl. ...

Hard Problems - Older Version · Added. 3:41. Hard Problems - Older Version. 9113 views. HardProblems · Bogan Pride - The Maths Olympiad 1/3 ...
25. ### YouTube - alyssaalexisbff's Channel

We also give tips and solve hard problems. Thank You!!!! p.s. even though me and Alexis fight were always bff's and it'll stay like dat 4EVER! ...

Hard Problems - Older Version. 10173 views. HardProblems · Paolo Villaggio Collection - Fantozzi (2° Parte) · Added to. Quicklist ...
27. ### YouTube - gojo66's Channel

She has only been bouldering for a year, but climbs some hard problems at F-red and HCR with a nice combination of technique and power. Enjoy ...
28. ### YouTube - Beautiful Young Minds - Saul's Quote

17 Oct 2007 ... Hard Problems - Older Version · Added. 3:41. Hard Problems - Older Version. 9076 views. HardProblems · Beautiful Young Minds - Cong's Quote ...
29. ### YouTube - Philosophy, Science and Math Documentary part 1

18 Jul 2009 ... Hard Problems Trailer - Updated · Added. 3:47. Hard Problems Trailer - Updated. 5937 views. HardProblems · Einstein's Brain part 1 ...

Hard Problems Trailer - Updated · Added. 3:47. Hard Problems Trailer - Updated. 5731 views. HardProblems · اذان - اصفهان · Added. 5:19. اذان - اصفهان ...
31. ### YouTube - IMO 2007 Highlights

Related Videos. Hard Problems Trailer - Updated · Added. 3:47. Hard Problems Trailer - Updated. 5458 views. HardProblems · IMO 2007 Basketball part#1 ...
32. ### YouTube - 2009 Raytheon MATHCOUNTS National Competition Highights ...

5 Aug 2009 ... 3:47. Hard Problems Trailer - Updated. 5892 views. HardProblems · I Think You're Wonderful, Red Grammer · Added. 2:42 ...
33. ### YouTube - Maths By Max

Hard Problems - Older Version. 9883 views. HardProblems · Pinoy students win silver, bronzes in China math olympiad · Added to. Quicklist ...
34. ### YouTube - Yoonie Challenge - Higher Maths

Hard Problems Trailer - Updated · Added to. Quicklist · 3:47 · Hard Problems Trailer - Updated. 6955 views. HardProblems · Higher Mathematics ...
35. ### YouTube - Harker School Intel Science Talent Search Semifinalists

16 Jan 2009 ... 3:47. Hard Problems Trailer - Updated. 5973 views. HardProblems · Harker Prom (Tiffany Lai, Rachel Yuan) ...
36. ### YouTube - Functions - How to sketch a complicated function

Hard Problems - Older Version. 9879 views. HardProblems · Watch Video on Domain and Range - Algebra Help · Added to. Quicklist ...
37. ### YouTube - FiveTenVids's Channel

2009 was not a disapointement with big names, hard problems and crazy lighting. music : "Fake Gold" and "Other Girls" ...
38. ### YouTube - PhotoFun Sample DONE

8 Oct 2009 ... Hard Problems Trailer - Updated · Added to. Quicklist · 3:47 · Hard Problems Trailer - Updated. 6998 views ...
39. ### YouTube - algebra dividing rational expressions 2 over 15

speaking, hard problems require better problem solvers. Sample list of problems: Rational discourse with fellow human beings: logic and math ...
40. ### YouTube - Gates Retirement Latest Challenge for Microsoft

... Associated PressAs Bill Gates ends his full-time tenure as Microsoft's leader, the software giant must face hard problems...
even he could not solve.
41. ### YouTube - IMO AGM, 9 O'Clock News, April 18, 2009

28 Feb 2009 ... Hard Problems - Older Version · Added. 3:41. Hard Problems - Older Version. 9188 views. HardProblems · TOEIC Listening test practice lesson ...