Through Mazes 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 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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