How to Calculate the Classical 7 Circuit Labyrinth

The question of a formula or table for calculating the construction elements in the labyrinth has arisen several times. For me, I solved the problem by designing and constructing the various labyrinths using a drawing program (AutoCAD). This creates drawings that contain all elements geometrically and mathematically exactly.
However, I do not print these on a specific scale, but adjust the size of the drawing so that it always fits on a sheet in A4 format.
Only the dimensions are decisive for the implementation of the labyrinth in the location. If possible, I also try not to use “crooked” measurements, but simple units, usually the meter.
The dimensions are therefore suitable to be scaled and so labyrinths can be constructed in different sizes.
The drawings thus represent a kind of prototype. Since the axes of the lines are always given, the widths of the boundary lines and the path can be varied.

The construction elements of the lines in the labyrinth mostly consist of arcs and straight lines. In the program used (AutoCAD), these individual elements can be combined into so-called polylines and their total length is then calculated.

The length specifications for the boundary lines and the path (the Ariadne thread) in the drawing are thus created. The boundary lines consist of 2 straight lines and 22 arcs (24 elements in total). The Ariadne thread consists of 1 straight line and 25 arcs (26 elements in total). The entire labyrinth consists of 50 individual elements.

It would be possible to calculate all of this in a table with the corresponding formulas, but it would be more cumbersome and extensive.

The scaling factor makes it easier to calculate variants in different sizes. The labyrinth calculator is something like a summary and general instructions for use. Here especially for the well-known Classical 7 circuit labyrinth.
However, this method has also been described for other types of labyrinths in this blog.

The Labyrinth Calculator

The Labyrinth Calculator

Here you can view, print or download the drawing as a PDF file

Here are some comments on copyright:
All drawings and photos in this blog are either mine or Andreas Frei, unless otherwise stated, and are subject to license CC BY-NC-SA 4.0
This means: You may use or change the drawings and photos without having to ask us if you name our names as authors, if you do not use the drawings and photos for commercial purposes and if you publish or distribute them under the same license. A link to this blog would be nice and we would be happy, but it is not a requirement.

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The Labyrinth on the Silver Coins of Knossos, Part 1

The silver coins of Knossos are quoted again and again when we talk about the labyrinth. They can be found in the major museums of the world.

Last year I was able to see and photograph one of them on a trip to Vienna in the Coin Cabinet of the Kunsthistorisches Museum.

Kinsthistorisches Museum Wien

Kinsthistorisches Museum Wien

The book “Labyrinths” by Hermann Kern shows illustrations of 20 coins from the British Museum in London.

Meanwhile there is a digital interactive catalog of the Coin Cabinet of the Staatliche Museen zu Berlinn, where you can access more than 34,000 coins.

With the search term “Labyrinth Knossos” I found 22, which I can show here under the following license.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Germany License.

The coins cover a period of 425 BC until 12 BC. Shown is mostly the reverse of the coin.

For the interpretation of the representations I have found some interesting information in the description that I quote here (translated from German):

The Cretan town of Knossos has been closely linked to the myth of the Minotaur since antiquity. His mythical dwelling, the labyrinth, was one of the city’s landmarks. However, the depiction of the labyrinth on the Knossos coins came in very different ways, since a real non-existing place had to be shown. The labyrinth is always pictured in supervision, but with different outer shapes and structuring. Only in supervision, the labyrinth can be detected as such.

I highly recommend visiting the digital catalog. There are to find many additional details about the coins. In particular, there is the possibility to look at both sides and to retrieve further information.

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Further Links

How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 1

Quite simply: By leaving off the barriers in the minor axes. I have already tried this with the Chartres labyrinth (see related posts below). But is that also possible with every other Medieval labyrinth?

As an example I have chosen the type Auxerre that Andreas showed here recently. This labyrinth is self dual as are Chartres and Reims, therefore of special quality. And they all have a complementary version.

The Auxerre labyrinth

The Auxerre labyrinth

Here the original with all the lines and the path in the labyrinth, Ariadne’s thread. The barriers in the minor axes are identical with those of the Chartres type. There is only another arrangement of the turning points (the lanes 4, 5, 7, 8) in the middle of the main axis.

The original Auxerre labyrinth without the barriers

The original Auxerre labyrinth without the barriers

The barriers are omitted. When drawing Ariadne’s thread, I found that four tracks could not be inserted. Hence, I have anew numbered the circuits and there remain now 7 circuits instead of the original 11. However, this also means that by changing this Medieval labyrinth into a concentric Classical labyrinth through this method no 11 circuit labyrinth is generated, but a 7 circuit.

The 7 circuit circular Cretan labyrinth

The 7 circuit circular Cretan labyrinth

If one looks more exactly at it, one recognises the well-known path sequence: 3-2-1-4-7-6-5-8. We got a Cretan labyrinth in concentric style.


Now we turn to the complementary labyrinth:

The complementary Auxerre labyrinth

The complementary Auxerre labyrinth

The complementary labyrinth is generated by mirroring the original one. The upper barriers remain, right and left they run differently and in the main axis, the turning points shift. The entrance into the labyrinth changes to the middle (lane 9) and the entrance into the center is from further out (lane 3).

The complementary Auxerre labyrinth without the barriers

The complementary Auxerre labyrinth without the barriers

As with the original, four lanes can not be inserted (4, 5, 7, 8). Therefore, the result is again a 7 circuit labyrinth. I renumbered the lanes and have redrawn the labyrinth.

This is how it now looks like:

The complementary 7 circuit circular Cretan labyrinth

The complementary 7 circuit circular Cretan labyrinth

The labyrinth is entered on the 5th lane, the center is reached from the 3rd lane. The path sequence is: 5-6-7-4-1-2-3-8. This labyrinth is not one of the historically known labyrinths. But it showed up in this blog several times (see related posts below). Because it belongs to the interesting labyrinths among the mathematically possible 7 circuit labyrinths.

The surprising fact is that no 11 circuit Classical labyrinth could be generated through the transformation. But for that  the 7 circuit Cretan labyrinth. Therefore we can say that the heart of the Medieval Auxerre labyrinth is the Cretan (Minoan) labyrinth as it is in the Chartres labyrinth.

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The Classical 7 Circuit Labyrinth with Crossed Axis

Andreas recently brought here a posting to the Jericho labyrinth St. Gallen which probably shows the historically first crossing of the main axis in a classical labyrinth.

I have written about that already. But now I would like to do it once again. Because for me it seems to be an element to design the labyrinth which I have not seen anywhere.

I became aware of that when I have no longer drawn the labyrinth from a seed pattern, but from the path sequence. And, besides, have noted that there also are different possibilities to connect the lines.

Using the example of the classical 7 circuit labyrinth I will explain this once again. How many possibilities to cross the axis are there, and how does it look like?

First the original labyrinth, however round and with a bigger middle.

The classical 7 circuit labyrinth

The classical 7 circuit Labyrinth

The last path sequence into the middle lies on the vertical main axis. The entrance lies on the left side of the main axis, leads to the third circuit, and turns to the left at first. The entry into the middle takes place from the fifth circuit from the right side, and faces the entrance.


How often can I now traverse the axis?
At two positions: From the first to the fourth circuit, and from the fourth to the seventh circuit. This can happen at each position alone or at both positions together. The result are three variations.

Here the first version:

Crossing the axis from the 1st to the 4th circuit

Crossing the axis from the 1st to the 4th circuit

By crossing the main axis from the first to the fourth circuit I do not change the direction of movement as in the original labyrinth. I am still turning to the left in the fourth circuit.
However, thereby I also reach the middle from the left side, so to speak I have laid this entry on the other side of the main axis.
The main entrance slides a little further to the left, and the two lower turning points also move to the left.


The second version:

Crossing the axis from the fourth to the seventh circuit

Crossing the axis from the fourth to the seventh circuit

Here the change from the first to the fourth circuit remains like in the original, however, from the fourth to the seventh circuit I maintain the “spin”.
The entry into the middle is executed from the left side as it is in the original. However, the main entrance slides to the right side. Both lower turning points are shifted to the right.


The third version:

Crossing the axis from the first to the fourth, and from the fourth to the seventh circuit

Crossing the axis from the first to the fourth, and from the fourth to the seventh circuit

The vertical main axis is crossed twice as in the previous versions, now together.
Through that the  lines are displaced considerably. Everything moves to the left. The main entrance lies again on the left side, the entry into the middle is made from the right side.


Here the path as Ariadne’s thread:

Ariadne's thread in familiar manner

Ariadne’s thread in familiar manner

Ariadne's thread with the axis crossed twice

Ariadne’s thread with the axis crossed twice

 

 

 

 

 

 

 

 

 

 

Maybe one can dismiss that as unnecessary? It would be nice, nevertheless to try it out in practice. Above all how it feels to experience another change of direction than in the original.

Maybe the opportunity arises in a big sandtable exercise? On a sandy beach for example? Where one can simply scratch the lines into the sand, and allows the flood to erase them out leniently.

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