Upcycled cardboard and duct tape Roman meander tiles

As things began to shut down for Covid-19 precautions, and our planned Hornby Island labyrinth workshops needed to be postponed, I got busy cutting up a big Amazon delivery box into 12" X 12" tiles and turning 16 of them into diagonally-striped Roman meander modular components. It was a satisfying way to make some fairly sturdy upcycled manipulatives to play with in designing this kind of labyrinth!

I thought about the idea of making a large playground installation with larger tiles of this sort that could swivel to create new labyrinth patterns. But my neighbour Alex, who saw me experimenting with this idea, pointed out that closely-packed squares don't swivel well (or at all), and the tiles would have to pop up or down to do so.

Reuleaux triangles, on the other hand, do swivel beautifully, but they don't tile the plane. <https://www.youtube.com/watch?v=-eQaF6OmWKw> Hmmm, how to work out a solution to this design problem?

Workshop with our UBC EDCP 551 class (Math, Language, the Body & the Arts) in the UBC Orchard Garden March 12

We held our graduate class in the UBC Orchard Garden teaching and learning garden and experimented with aspects of mathematical thinking with labyrinth design:

• We tried out different 'seeds' for classical labyrinths, experimenting with keeping some things invariant and varying others, and predicting the resulting labyrinths.
• We tried creating asymmetrical seeds, with even or odd numbers of attachment points; joining attachment points more and less symmetrically; trying to create new star-shaped seeds, and more.
• We tried out our first set of striped tiles to create a Roman meander-type labyrinth, with interesting results! (The edges were tricky and might need some triangles...) 
• We accomplished the exciting Gardner's Double Appleton Labyrinth Dance on our sidewalk chalk labyrinth. (Follow link to video)

Workshop with Burnaby teachers on February 28 2020 Pro D

We had a wonderful workshop with Burnaby elementary and secondary teachers on Friday February 28 in the dance lab at Burnaby North Secondary School. Fifteen teachers and teacher librarians participated (about half from elementary and middle years and half from secondary). We introduced the historical and modern contexts of labyrinths, experimented with drawing and predicting the shapes of classical labyrinths from different seeds, made a large labyrinth on a 20' square large tarp, and successfully did the Gardner's Double Appleton Labyrinth Dance (with a few experimental moments, naturally)! (Follow link to video).

Many thanks to Burnaby Science and Math Coordinator Donna Morgan, and Pro D Coordinators including Mati Bernabei and Phil Byrne and all the participants for a satisfying and successful learning experience.

Slides from our presentation

These slides include a brief history of labyrinths and a step-by-step how to draw a classical labyrinthfrom a simple seed pattern (and variations on the seed). 

The Labyrinth Society website & local labyrinth resources

Did you know that there is an International Labyrinth Society, with an informative website and annual meetings?

There are quite a few existing labyrinths in the Lower Mainland and on Vancouver Island -- for just a few examples, the St. Paul's Anglican Church painted labyrinth in Vancouver's West End ( a replica of the Chartres Cathedral labyrinth), and a whole tour of labyrinths on the Island.

Did you know that the Bethlehem Centre in Nanaimo houses Bill Godden's collection of Finger Labyrinths -- a finger labyrinth museum? Finger labyrinths can help plan labyrinth designs, and are sometimes used as a way for people (including kids) to calm an anxious mind by 'walking' a labyrinth in miniature with hands.

There are labyrinth designers and historians all around the Lower Mainland, Vancouver Island and around BC.

Here's another excellent resource for those who want to try their hand at designing and building a labyrinth!.

More excellent resources on labyrinths, their history and construction

Most of these interesting books are available via Amazon.ca and other online sources!

A write-up, animation and film of Gardner's Double Appleton labyrinth dance

How can it be geometrically possible to have two (or even three) people walk a labyrinth hand in hand (in hand) when some are going in toward the centre, and others are going out the the finish?

Grahame Gardner has worked out the logic of this labyrinth dance in 2011, based on Appleton's original form.

The write up of Gardner's Double Appleton is here, on Gardner's blog.

The film illustrating Gardner's Double Appleton is here.

Fascinating! We're looking forward to trying this on our own labyrinth.

Labyrinths are ancient, fascinating and mathematical

Note the difference between mazes (which have high walls, dead ends and many potential wrong turns) and contemporary labyrinths (often a very low or flat design on the ground that encourages contemplative walking. Labyrinths are unicursal (i.e. having a single path) and often in the shape of some kind of spiral. They often lead in to a resting place near the centre, so that the labyrinth walker has a phase of going in, a phase of resting or meditation, and a phase of going out of the path.

Here are some great resources to start learning about the history of labyrinths and math:

1. Chapter from the MAA book, Hands On History, about the history and geometry of traditional labyrinths.  (Here's a scan of it too.)
   
   
   
2. A Bridges Math and Art 2013 conference paper (Fenyvesi, Jablan & Radovic) that shows a way to construct labyrinths out of striped squares -- something that would be interesting to try with a class.
   
   
   
   
   
   
   
   
   
3. Making Your Own Labyrinth The Easy Way: Anne Nesbitt, 2003.