The Labyrinth Society website

 Here's the link to the very helpful and interesting website of the international Labyrinth Society. They
hold an annual labyrinth gathering that I'd like to attend one of these years. 

There are lots of excellent links to films, papers, maps and discussions here.

Interesting films about magics squares and labyrinths from our presentation and beyond

 The Mathologer on the Korean king's method of constructing odd-order magic
squares: https://www.youtube.com/watch?v=FANbncTMCGc

Gardner's Double Appleton labyrinth dance:https://www.youtube.com/watch?v=nXS-U0HZn1M

Susan & company's film about community labyrinthn workshops on Hornby Island (Bridges 2022 Short Film Festival link): https://gallery.bridgesmathart.org/exhibitions/2022-bridges-conference-short-film-festival/susan-gerofsky

A video of a talk by John Conway on magic squares from the 2014 Gathering for Gardner (related to his 2015 Bridges talk, which was unfortunately not recorded): https://www.youtube.com/watch?v=ZK-RXLJT7eM

Slides from our 2025 Bridges Eindhoven workshop

 Here's a link to a PDF of the slides!

Examples of magic squares -- planetary and non-planetary

 Here's a link to the 33 pages of (random) magic squares that we used in our colouring activity in the
workshop.

It's interesting to note that there doesn't yet exist a general magic square generator online. You can find some generators, but they keep reproducing the same squares according to some particular algorithm. Considering that there are so many possible magic squares of different dimensions, it seems as though there ought to be a generating program available.  We think that there is also a great need for  comprehensive ways of categorizing all the magic squares to help us understand how they work and what patterns they embody!

Some very good resources for further exploration of labyrinths and magic squares

 

Some recommended books on labyrinths. 

• The Jeff Saward book is an excellent overview, and is the source of the world map of labyrinths and mazes used in our slides. 
• The Hermann Kern book is a huge compendium of information about labyrinths -- and also contains Robert Ferré's claim about magic squares and labyrinth seeds (as does the Ferré book!)

Here is the reference list from our Bridges 2025 workshop paper. Sorry that the type came out so dark here, but you can check these links on the Bridges 2025 papers archive link to our workshop paper at https://archive.bridgesmathart.org/2025/bridges2025-581.html#gsc.tab=0

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!