5 April 1999 Vol. 4, No. 14
THE MATH FORUM INTERNET NEWS
Math Awareness Month (MAM) | Kepler Conjecture |
Chaos - Interactive Mathematics Online
MATH AWARENESS MONTH (MAM)
http://mathforum.org/mam/
April is Math Awareness Month. This year's theme is
Mathematics and Biology, with essays on "Math in the Heart"
by Dr. James Paul Keener of the University of Utah, and
"Math and DNA" by Dr. De Witt Sumners of Florida State
University.
Dr. Louis J. Gross of the University of Tennessee has
provided two new essays, "How Does Biology Affect
Mathematics?" and "Mathematics and Ecology." With
assistance from the Education Committee of the Society
for Mathematical Biology, an extension of the Quantitative
Curriculum for Life Science Students project, Dr. Gross has
also collected resources for mathematics education for
biology students collected.
http://mathforum.org/mam/99/resources/
Read about outreach activities at institutions nationwide
and submit an announcement to see your event included in
the list.
http://mathforum.org/mam/activities/
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THE KEPLER CONJECTURE
The Kepler Conjecture, a 400-year-old problem posed in 1611
by the astronomer Johannes Kepler, investigates the most
efficient way to pack equal-sized spheres: in identical
layers one on top of the other, each sphere in a higher
layer directly above the sphere directly beneath it, or
staggering the layers so that spheres in each higher layer
sit in the hollows made by the spheres beneath them.
Kepler posited that no packing of equal-sized spheres in
space can have greater density than that of the face-centered
cubic lattice packing - a conjecture which, like Fermat's
Last Theorem, has long been easier to state than to prove,
but for which a proof has now been offered. Sites to explore
include:
- The Kepler Conjecture - Hales, Ferguson
http://www.math.lsa.umich.edu/~hales/countdown/
The authors claim to have proved the Kepler Conjecture;
the full proof is included in over 250 pages in postscript
format, with background, history, popular and academic
articles, and software tools used in the proof. For a
brief explanation, see What is the Kepler Conjecture?
http://www.math.lsa.umich.edu/~hales/countdown/what.html
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ARTICLES DESCRIBING AND DISCUSSING THE PROBLEM
AND THE PROOF
- Kepler's Sphere Packing Problem Solved - Keith Devlin
http://www.maa.org/devlin/devlin_9_98.html
An article from Devlin's Angle (MAA Online), describing
the problem and discussing the proof.
- Cracking Kepler's sphere-packing problem - Ivars Peterson
http://www.sciencenews.org/sn_arc98/8_15_98/fob7.htm
An article from Science News Online.
WHAT IS MATHEMATICAL PROOF?
- Proof is out there - Keith Devlin
http://go2.guardian.co.uk/science/906551943-kepler.html
An article from The Guardian Online's Science section
about cases, such as the solution to Kepler's Conjecture,
that raise the whole question of what constitutes a
mathematical proof.
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CHAOS - INTERACTIVE MATHEMATICS ONLINE
Eger, Garmendia, Champaneria
http://tqd.advanced.org/2647/chaos/chaos.htm
Think of any system that changes over time - the weather, the
stock market, or the genetic distribution of a population.
Whatever dynamical system you choose, Chaos Theory (the
mathematical proofs and theories that attempt to describe
processes in motion) can be used to understand it.
The contents of this site include:
- basic concepts - iteration; orbits; attraction and
repulsion; graphical analysis; bifurcations
- examples - Cantor Set; Sierpinski Triangle; Mandelbrot
Set; Julia Set
- Java applets involving chaos - Mandelbrot/Julia Set
Explorer; Mandelbrot Escape Sequences
This 1996 ThinkQuest Junior entry also offers material on
algebra, geometry, stereograms, and "Cool Java Stuff," a
"starter kit" for those interested in learning Java.
http://tqd.advanced.org/2647/
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