David Thompson & Diana ChengTowson University

What does Mathematics have to do with Mazes?

Where have you seen mazes?

Greek mythology: Theseus entered a labyrinth & killed the Minotaur

Mazes around the world

Cathedrale Notre Dame de Chartres, France (medieval)

Hopi Indians’ penta-seed pattern (classical)

4000 year old concept

http://labyrinthlocator.com/home

Baltimore area: JHU Bayview St John’s Lutheran Church (Parkville) Stevenson University’s Greenspring

Campus - Menning Meditation Center and Labyrinth

Find a maze near you!

Definition & example

Labyrinths

Exactly one way in to the center & the same way out

Properties: Circuits (7) Seed pattern

(square)

3 & 7 Circuit Labyrinths

11 & 15 Circuit Labyrinths

19 & 23 Circuit Labyrinths

compass – centers of quarter circles in A, B, C, D, E

Construction of Classical Labyrinths

A

CD

E B

Partitioning of the 7-circuit labyrinth

Solution pathsExample: 3-circuit’s path: 3, 2, 1, 0

Solution pathsWhat patterns do you notice?

The kth circuit in the solution path is fk(C). The fk(C)th circuit in the solution path is k.

2c.

Thompson, D. & Cheng, D. Growing labyrinths from seeds. (September-October 2015) The Oregon Mathematics Teacher, pp. 33-36.

Thompson, D. & Cheng, D. Square Seeds and Round Paths: Exploring Patterns with the Art of Classical Labyrinths. Published in conference proceedings of BRIDGES 2015: Mathematics, Music, Art, Architecture, Culture. Baltimore, MD. Available online at

http://archive.bridgesmathart.org/2015/bridges2015-555.html

References

Contemporary TSP labyrinths