Many are surprised how long the way in a labyrinth can be, especially if they walking labyrinth for the first time. And many who want to build a labyrinth, e.g., with stones or with candles, are astonished how much material they need.
Under the heading “Principles of Form” in his book Labyrinths Hermann Kern writes about the >tortuous path principle<:
– if the path fills the entire interior space by wending its way in the most circuitous fashion possible
If I stand ahead of a labyrinth, the middle, the goal is within my reach. However, only when walking in I get to know how winding and complicated the way is in reality. But yet, this way, the red thread or Ariadne’s Thread is the continuous line in the labyrinth, without crossroads or junctions.
In the drawing I call “A” the beginning of the path and “Z” the goal, the center or middle. In many labyrinths I could reach directly the middle with a few steps across all limitations. But this is not really what is intended with a labyrinth.
Now I compare for a 7 circuit labyrinth with a diameter of about 15 m the short way (direct connection between A and Z) with the long way along the Ariadne’s Thread. The length of the short way amounts to 6.33 m, the long way has a length of 154.62 m. Or differently expressed: The long way is 24.4 times longer than the short way (154.62: 6.33 = 24.4).
One could also see in this a formula for the labyrinth. To calculate how powerful is the layout for example. Or how wended is the way? Or from what minimal surface area I can extract which maximal length?
Maybe one could call this value in honour of Hermann Kern “detour factor” 24.4?
If I handle this thread at the beginning and at the end and pull it apart, I will get a straight line which reaches from “A” to” Z” and is as long as the way inside the labyrinth, i.e. 154.62 m.
I can arrange this to a circle. The perimeter corresponds to the straight line of 154.62 m. The resulting diameter would be 49.22 m.
I can also make a square with the same extent from it. Then this would have four side lengths of 38.65 m.
The following drawing, yet not true to scale, illustrates the different figures and the true ratios among each other: