Welcome to the workshop on magic squares & labyrinth seeds

 Our workshop paper, Exploring an Open Question About Magic Squares and Classical Labyrinth Seed Patterns, is available in the Bridges Archive. The paper was co-authored by Susan Gerofsky, Asia Matthews, Helen Lambourne, Tony Law, and Tara Taylor; Susan and Tara are leading the workshop today.

We have all been involved with labyrinths for several years now: 

• exploring their mathematical properties
• finding out what we can about their fascinating worldwide history
• sharing our findings with others: our students (K-16) and our intergenerational communities

We have taken a special interest in so-called 'classical labyrinths', one of the most ancient forms of labyrinth that can be generated from an unlikely-looking (but effective) geometric seed. The most commonly found classical labyrinth is the 7-course labyrinth generated from the following seed:

This paper and workshop were initiated in response to a provocative claim connecting these labyrinth seeds with magic squares, published in several books by labyrinth scholar Robert Ferré:

There is another aspect of the seed pattern that I find mind boggling. It has to do with magic squares... In a magic square, each column and row add up to the exact same sum, as do the diagonals... Many of them were assigned the names of heavenly bodies. The one I want to describe is the Square of the Moon [degree 9]... Suppose we mark all the odd numbers in the magic square. What happens? We get the seed pattern for a classical labyrinth! I have no idea why or how that happens. All magic squares with an odd number of squares, 5x5, 7x7, 9x9, etc., exhibit this phenomenon [or so Ferré claims: SG] Those with an even number of squares such as 6x6, 8x8, do not form a seed pattern. Instead, they make a checkerboard pattern, which I find no less puzzling. (pp. 43–44)

The geometric seed for a 7-course classical labyrinth & the 9x9 "planetary" magic square: why does this pattern appear in both of these constructions? 

 In this workshop, we will explore classical labyrinths, magic squares, and the open question about Ferré's claim!