Volume 2, Number 27

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 Java-capable browser is required): - Tic-Tac-Toe - Maze - Crossword - Word Search - Jigsaw - Chess In addition, a "Topo Map" applet lets you construct your own topographical map, revealing the topology of the 2-dimensional space in which it is drawn. These applets are being developed for Bolt, Beranek and Newman Inc. as part of the NSF-funded curriculum development project, Teaching Mathematical Thinking through Computer-Assisted Space Explorations. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- GEOMETRY THROUGH ART - NORMAN SHAPIRO http://mathforum.org/~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://mathforum.org/web.units.html -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 multi-million-dollar 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/mega-math/workbk/map/map.html - Activities: stories and a two-colorable 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 problem-solving process, induction - Materials and Preparation: maps to print out for coloring - For Further Study: other types of puzzles \|/ For a more advanced presentation, see THE FOUR COLOR THEOREM, which has a brief summary of a new proof of the theorem and a four-coloring 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 four-color 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problem of the Week http://mathforum.org/geopow/ Internet Resources http://mathforum.org/~steve/ 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\ / \ / \ / | / \ / \

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