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Newsletter: Math Forum Internet News No. 2.27 (July 7)
Posted:
Jul 5, 1997 12:42 PM


7 July 1997 Vol.2, No.27
THE MATH FORUM INTERNET NEWS
Topology Games  Geometry through Art  Four Color Theorem
TOPOLOGY GAMES  JEFF WEEKS
http://www.northnet.org/weeks/
The torus and Klein bottle are introduced through six simple games (a Javacapable browser is required):
 TicTacToe  Maze  Crossword  Word Search  Jigsaw  Chess
In addition, a 'Topo Map' applet lets you construct your own topographical map, revealing the topology of the 2dimensional space in which it is drawn.
These applets are being developed for Bolt, Beranek and Newman Inc. as part of the NSFfunded curriculum development project, Teaching Mathematical Thinking through ComputerAssisted Space Explorations.
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GEOMETRY THROUGH ART  NORMAN SHAPIRO
http://forum.swarthmore.edu/~sarah/shapiro/
Art is one of the intrinsically interesting applications of geometry, and these pages provide an interdisciplinary way for children and adults alike to approach the subject.
Artist/Educator Norman Shapiro treats the student as an investigator and emphasizes learning through doing. He uses perception to stimulate the motivation for more fully developed concepts and language. The unit includes lesson ideas, suggestions for facilitation, lists of materials needed, colorful and detailed illustrations, and handouts to photocopy.
Geometry through Art is one of a number of Math Forum Web units described at:
http://forum.swarthmore.edu/web.units.html
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FOUR COLOR THEOREM
"Dear Dr. Math  What is the four color theorem? I know it has something to do with math!"
Coloring is a mathematical topic with multimilliondollar industrial applications, and the four color map theorem has engaged mathematicians for over a hundred years. MEGAMATH, a project of the Computer Research and Applications Group at Los Alamos National Laboratory, features a group of Web pages about THE MOST COLORFUL MATH OF ALL:
http://www.cs.uidaho.edu/~casey931/megamath/workbk/map/map.html
 Activities: stories and a twocolorable map  Big Ideas and Key Concepts: mathematical proof  Background Information: the math behind the maps  Vocabulary: map, region, boundary...  NCTM: links to the Standards  Evaluation: the problemsolving process, induction  Materials and Preparation: maps to print out for coloring  For Further Study: other types of puzzles
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For a more advanced presentation, see THE FOUR COLOR THEOREM, which has a brief summary of a new proof of the theorem and a fourcoloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas, of Georgia Tech:
http://www.math.gatech.edu/~thomas/FC/fourcolor.html
In addition to a fourcolor map of the United States, the contents include:
 History  Why a new proof?  Outline of the proof  Main features  Configurations  Discharging rules  Pointers  A quadratic algorithm  Discussion and References
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The Math Forum ** 7 July 1997
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