Knidos is a Style
Knidos is not a type but a style. Just as well as for instance the classical, concentric or MiM-style.
This becomes already evident from the fact that Erwin has published several types of one arm labyrinths in the Knidos style, among others the Knossos type, the Cretan, the Otfrid tye (see below, related posts: “How to build a Labyrinth in Meander Technique”).
Erwin was inspired by a labyrinth example on a rock carving from Knidos, hence the name. This labyrinth is an early attempt of a Cretan type on a concentric layout.
In his post “How to Make a Knidos Labyrinth” (see related posts), Erwin describes how he developed a geometrically exact labyrinth based on this example. The result is a Cretan type labyrinth in the Knidos style (fig. 3).
In a later even more interesting post “How to Draw a Labyrinth” (see related posts), Erwin has generalized the method and described it more in detail. For this he has used a non-alternating labyrinth with the level sequence 3 2 1 4 7 6 5, and thus did not use the Cretan type labyrinth. First, the Ariadne’s Thread is drawn freehand. Also from this it follows, that “Knidos” is a style and not a type. With the Ariadne’s Thread the type of labyrinth is already given, before it has been designed in the appropriate style. This is then performed in the following steps.
Here I will show the Knidos style using the same figure I have used in my last post for the presentation of the styles (see related posts). I will abbreviate the description of the method and highlight the central elements of this style.
In fig. 4 the Ariadne’s Thread “drawn freehand” can be seen in red. By this, the type to be drawn in the Knidos style is already defined. Now we add three auxiliary circles with radii of 1, 2, and 3 units around a point in the center. The unit 1 is the equivalent of the width of the pathway including one of the walls delimiting the pathway. The distance between the point in the middle and the innermost auxiliary circle and then between subsequent circles is always one unit.
Next, we have to determine the situation of the turning points. Our simple figure has only two turning points (W1 and W2).
The situation of the turning points is determined by means of construction lines. One lies at the end of the inner (W2), the other at the end of the outer (W1) wall delimiting the pathway. The center is four units wide. Therefore the innermost wall delimiting the pathway lies on the second inner auxiliary circle. And, as the figure has only one circuit, the outermost wall lies on the third auxiliary circle. The distance between the center (M) and turning point W2 is 2 units, and 3 units between he center and W1. This is determined by their situation on the auxiliary circles. But what is the distance between W1 and W2?
Here the special property of the Knidos Style becomes apparent. All construction lines are integral multiples of the unit long. Their length is determined by the number of segments of the Ariadne’s Thread between two turning points. Between W1 and W2 there are two such segments. Therefore the distance between W1 and W2 is two units. We thus have to move both turning points along their auxiliary circles until they have reached an exact distance of two units.
The construction lines fit together to a polygon (in our case a triangle). This connects the center with the turning points. For the length of the construction lines between the turning points and the center, two units have to be added to the number calculated as described above, due to the enlarged area around the center. The resulting triangle has sides with lenghts of 3 (M – W1), 2 (W1 – W2) and 2 (W2 – M) units. By this, all points are determined relative to each other. This also works in labyrinth types with more than two turning points.
That is ingenious!
This polygon can now be rotated around the center. By this it is possible to align the axis as desired. Erwin aligns the segment of the pathway, that leads to the center, centrally on the central axis.
For this, as shown in fig. 6, the triangle must be rotated around the center in such a way that the turning point W2, where the pathway turns off to the center, comes to lie ½ unit to the right of the central axis. The situation of W1 is then given as a result of this position.
Fig. 7 finally shows how the figure is finalized. For this, from the turning points, auxiliary circles with a radius of 1 unit are inscribed. Then on these auxiliary circles, arcs of circles are drawn that connect the walls delimiting the pathway with the construction line between the turning points.
With “Knidos”, Erwin has developed a extraordinary way of the gaphical design of labyrinths. This can be justifiably classified as a style. While I have stated in my last post, that style cannot be determined as exactly as type, this is true for style in general. However, individual styles may be excepted. This applies to the Knidos style. This style is geometrically exact, fully determined by the relations of multiple integrals of the width of the pathway and can be designed using only compass and ruler.