Recently you could read something about the long and winding path in a classical labyrinth.

Today we want to look more exactly at the path in the Chartres labyrinth. This is quite an other type of labyrinth. It has more circuits than the Cretan labyrinth, eleven instead of seven.

We orientate by the original, that is since about 800 years on the floor inside the cathedral of Chartres. The ways are much smaller than they should be for a “open land labyrinth”.

It depends not only on the type labyrinth, how long the ways are, but also from the constructive form. So: How wide the ways are, how wide the boundary lines are in between, how big the middle is etc.

In the Chartres labyrinth we have a distance of 42.6 cm from axis to axis.

From A to Z: The long and the short path

The direct way from “A” to “Z” straight across all boundary lines to the center of the Chartres labyrinth amounts to 6.45 m. This corresponds to half a diameter of 12.90 m.

The whole, long way from the entrance into the center amounts to 263.05 m by following all the turns. This proves a relation between the long and the short distance of 263.05: 6.45 = 40.78. So a much higher “detour factor” than in the Cretan labyrinth.

If I handle the thread at the beginning and at the end and stretch it apart, I will get a straight line which reaches from “A” to “Z” and which corresponds to the way into the middle, that is 263.05 m.

If I join together the beginning and the end, I will get a circle. The circumference corresponds to the straight line of 263.05 m. The diameter would be 83.73 m.

I can also make a square with the same size from it. Then this would have four side lengths of 65.76 m.

The following drawing, yet not true to scale, illustrates the different figures and the true ratio among each other:

Ariadne’s Thread unrolled

Don’t be surprised that the original labyrinth looks so tiny. This is due to the “detour factor” of 40.78. (To keep in memory: For the Cretan labyrinth this value amounts to 24.4).

The unrolled thread of Ariadne is much longer relative to the original labyrinth. The proportions in the drawing however are right.

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