Math Forum Internet News

Volume 2, Number 27

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  7 July 1997                                 Vol. 2, No. 27


Topology Games | Geometry through Art | Four Color Theorem



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.



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:


                    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

  - 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:

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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