The Mathematics of Labyrinths

David Thompson & Diana ChengTowson University

Definition & example

Labyrinths

Maze: One way in One way out

Properties: Circuits (7) Seed pattern (square)

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

Labyrinths in architecture & art

Serpentine mosaic labyrinth in Paphos, Cyprus (Roman)

Kabala or “Tree of Life” labyrinth (classical)

Contemporary labyrinths

Tim Chartier’s (2014) Math Bytes labyrinths

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 labyrinth near you!

Compass & straightedge GSP SP

Construction of Classical Labyrinths

1. Construct a Square2. Construct the midpoints & connect opposite

midpoints

From Each Midpoint to the end point of the square dilate each point by a ½ ratio

Create a Cross and find the center of the labyrinth

Using the center of the labyrinth construct an arc on circle extend points as necessary(arc on

circle)

Create the quarter circles to complete the circuits (arc through 3 points)

Construct the lower quarter circles(Extend the lower part of the square arc through 3 points)

Hide all points except corners of square

Color the labyrinth using the exterior arcs (semi circle, 2 upper and 2 lower quarter cirlces) and

square

# 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

3 & 7 Circuit Labyrinths

11 & 15 Circuit Labyrinths

19 & 23 Circuit Labyrinths

# circuits vs. # dilated points

# circuits vs. # interior intersection dots

Radius vs. Length of outer semi-circle radius

Arc length vs. # circuits

Area of labyrinth

Dilations

Equations of semi-circles

Equations of semi-circles (part 2)