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Topic: Newsletter: Math Forum Internet News No. 2.27 (July 7)
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Sarah Seastone

Posts: 1,240
Registered: 12/3/04
Newsletter: Math Forum Internet News No. 2.27 (July 7)
Posted: Jul 5, 1997 12:42 PM
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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.


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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 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

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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 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


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CHECK OUT OUR WEB SITE:

The Math Forum http://forum.swarthmore.edu/
Ask Dr. Math http://forum.swarthmore.edu/dr.math/
Problem of the Week http://forum.swarthmore.edu/geopow/
Internet Resources http://forum.swarthmore.edu/~steve/
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The Math Forum ** 7 July 1997

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