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to Mathematics

Build your own labyrinth:
A class activity using the nesting of segments on the
number line.
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 prehistoric
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 8level 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 12level
labyrinth. Since there are 262 different 10level labyrinths,
and 1828 different 12level 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 butcherpaper to cover an 18 x 21 foot area.
 1.5 or 2"wide masking tape, three or four thick markerpens.
 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