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.
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.