After the discovery of the Knidos labyrinth the geometry and the exact construction is asked.
There are classical labyrinths with a larger center since longer, also as walkable labyrinths. However I noticed that were certain artistic freedoms to design them. For instance that the turning points are not in a square, or that the central cross is displaced, or the ways are differently broad.
After longer trying I found out how one can design best (at least in my opinion) geometrically and mathematically exactly a classical labyrinth with a larger center (that I call from now on Knidos labyrinth).
In practice the quadruple of the way’s width is a good measure for the center. That is also the measure for the four turning points of the internal square, on which these are situated. The sizes of the circle of the center and the square have thus a good purchase within the labyrinth.
All lines of the labyrinth ways and the way axes are circular arcs, which are clashing without break. The segments, within those the circular arcs with the same center are lying, result from the lines through the 5 centers of the labyrinth.
Maybe the drawings shows more simply what in words sounds so complicated.
That is the basic structure of the construction. In the classical labyrinth the center for the upper arcs is between the two upper corner points of the square. In the Knidos labyrinth this center (marked with M1) goes upwards. The distance M2-M1 is fourfold the way’s width (2 ways + the half center); the distance M3-M1 is threefold the way’s width (1 way + the half center).
The lengthenings of the aforementioned distances form at the same time the delimitation of the upper 8 circular arcs, which have all their center in M1. The further segments are built by lengthenings of the distances M2-M4 and M3-M5. The points M2 to M5 are both the turning points of the labyrinth as well as the centers of the further circular arcs.
With M2 as center all free ends of the preceding arcs on the left side are connected. The three lower arcs end at the line M2-M4.
The same happens on the right side, whereby the lower 4 arcs end at the line M3-M5.
Around the center M4 a semi-circle connects two further open ends of the preceding arcs. A quarter circle around M4 connects the lower free end of the central cross with the left end of the central cross.
Four further semi-circles around the center M5 connect the three open ends on the right side and the right end of the central cross. Thus the construction of the labyrinth is finished.
Here again the whole labyrinth without the auxiliary lines. The central lozenge is the result when all ways are designed in same width.
- The Knidos Labyrinth
- The Knidos Labyrinth Prototype
- How to build a Knidos Labyrinth with Bark Mulch
- How to build a Knidos Labyrinth with Paving Stones