10 May 1999 Vol. 4, No. 19
THE MATH FORUM INTERNET NEWS
UBUYACAR  Maricopa  Rubik's Cube  Math Ideas in Science  7 Stones
UBUYACAR  Maricopa Center for Learning and Instruction
http://www.mcli.dist.maricopa.edu/pbl/ubuystudent/
You are interested in purchasing a new vehicle.
Can you afford the one you want? To buy it,
what should your annual salary be?
An online problembased learning manual for students, part
of Maricopa Community College's Problem Based Learning
(PBL) site.
http://www.mcli.dist.maricopa.edu/pbl/
Students move through a problemsolving process, while a
Tutor's Manual coaches the teacher in the role of
facilitator.
http://www.mcli.dist.maricopa.edu/pbl/ubuytutor/
The manuals are also available in PDF format.
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RUBIK'S CUBE
Questions about Rubik's cube are frequently posted to math
discussion groups archived by the Math Forum. Here are some
sites that may be helpful for those interested in solving
this puzzle:
 RUBIK'S CUBE INFORMATION  Michael Reid
http://www.math.brown.edu/~reid/rubik/
links to pages, notes, solutions, interactive cubes
on the Web, books, software, and algorithms
 RUBIK'S CUBE  Georges Helm
http://ourworld.compuserve.com/homepages/Georges_Helm/cubeold.htm
600 solutions to 2x2x2, 3x3x3, 4x4x4, and 5x5x5 cubes,
pyraminx, and barrel
 HOW TO SOLVE THE RUBIK'S CUBE 2.0  Mark Jeays
http://www.ncf.carleton.ca/~ad161/rubiks.html
a complete solution to solving the cube starting from
any position, based on the 1980 book Notes on Rubik's
Magic Cube
 THE MATHEMATICS OF THE RUBIK'S CUBE  W. D. Joyner
http://web.usna.navy.mil/~wdj/rubik_nts.htm
lecture notes for a course given at the U.S. Naval Academy,
available in LaTex and ASCII versions and including an
introduction; chapters on logic, functions on sets,
permutations and permutation puzzles, some solution
strategies, groups, orbits, actions, and cosets, Cayley
graphs and God's algorithm, symmetry groups of the Platonic
solids, structure of the Rubik's cube group, Rubika
esoterica, and realizing PGL(2,F5) inside the Rubik's
cube group; and references
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To find more sites about the Rubik's cube, use the Forum's
Math Library searcher to look for the word Rubik:
http://mathforum.org/library/#search
For conversations about solving Rubik's cube, search all
epigone discussions of groups archived by the Math Forum:
http://mathforum.org/discussions/
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MATHEMATICAL IDEAS IN SCIENCE  Seven Stones Multimedia
http://www.7stones.com/Homepage/Publisher/Tut01.html
A series of tutorial modules using JavaScript, Shockwave
for Director, or Shockwave Flash, designed to help clarify
some complex ideas in mathematics and science. Contents
include:
 sphere packings
 shapes and lattices
 waves and harmonic disturbance
 vectors, projectile motion, planetary orbits
 octonion and division algebras; lie algebras, groups,
and spinors (Clifford algebras)
 special relativity
 quantum mechanics, uncertainty, nuclear decay and
halflife, Bohr atoms
 statistics (linear regression)
 astronomy (expanding universe, Doppler shift)
More information is available from the Seven Stones home page:
http://www.7stones.com/Homepage/sevenhome2.html
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