1. The Mathematics of Labyrinths
David Thompson & Diana Cheng
Towson University
2. Definition & example
Labyrinths
Maze:
One way in
One way out
Properties:
Circuits (7)
Seed pattern (square)
3. Greek mythology: Theseus entered a labyrinth & killed the Minotaur
Labyrinths around the world
Cathedrale Notre Dame de
Chartres, France (medieval)
Hopi Indians’
penta-seed pattern
(classical)
4000 year old concept
4. Labyrinths in architecture & art
Serpentine mosaic labyrinth in
Paphos, Cyprus (Roman)
Kabala or “Tree of Life”
labyrinth (classical)
11. Using the center of the labyrinth
construct an arc on circle extend
points as necessary(arc on circle)
12. Create the quarter circles to
complete the circuits (arc through 3
points)
13. Construct the lower quarter circles
(Extend the lower part of the square arc through 3 points)
Hide all points except corners of square
14. Color the labyrinth using the exterior arcs
(semi circle, 2 upper and 2 lower quarter
cirlces) and square
15. # of circuits and:
# of dilated points in inner square
# of interior intersection dots
Radius & length of outer semi-circle radius
Arc length & # circuits
Area of labyrinth
Dilations
Equations of semi-circles
Math within labyrinths