Tony Phillips, Math Dept SUNY Stony Brook
tony at math.stonybrook.edu
The activity described on these pages is suitable for students
from grade 6 on. For younger students, try
Exploring Labyrinths.
Labyrinths (the word used here for a special kind of maze)
have been constructed and enjoyed by people since pre-historic
times. Recently a way has been found to encode these patterns
numerically, and to use the mathematical formulation to
study existing labyrinths and to generate new ones.
Outline:
- First,
students will learn how to draw the Cretan
maze. This 8-level labyrinth is the oldest one of all; the
pattern of its windings, and the way they are generated from a
simple ``nucleus,'' are still fascinating.
- Then they will
discover the level sequence of this labyrinth (it is
0 3 2 1 4 7 6 5 8), and will be shown the criteria which allow
a sequence of numbers to be the level sequence of
a labyrinth.
- Next the class and the teacher together
will apply these criteria to construct a 10 or 12-level
labyrinth. Since there are 262 different 10-level labyrinths,
and 1828 different 12-level labyrinths,
there is a chance theirs will be one that has never been seen
before.
- Finally
the class will draw their new labyrinth on
the floor and will experience it directly by walking
through it.
Supplies:
- Each student should have a pencil and a few sheets of paper. A sheet
of graph paper is useful.
- Blackboard or OHP for teacher. Colored chalk useful.
- Newsprint or butcher-paper to cover an 18 x 21 foot area.
- 1.5 or 2"-wide masking tape, three or four thick marker-pens.
- Music for maze perambulation: something very calm, like
Satie's ``Gymnopédies,'' on piano or recorded.
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Tony Phillips
tony at math.stonybrook.edu
January 7, 1999