### Volume 4, Number 14

 ``` 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/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 \|/ 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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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/ -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/pow/ Mathematics Library http://mathforum.org/library/ Teacher2Teacher http://mathforum.org/t2t/ Discussion Groups http://mathforum.org/discussions/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ ```