-Three Wise Men Labyrinths- Basic, Bronze, Silver, and Gold
-Article By-
Giacomo Aureo, 2021.
A series of square labyrinths where 3 equal length parallel diagonal lines connect the open corner to the center section, coined: Three Wise Men Labyrinths.
The mouth, or open corner, has the same dimensions as the central portion, the neck and tail portions of the path are equal to each other, and the rest of the path is of consistent width in relation to the straights and corners.
When using whole numbers on a grid, 7x7 is the smallest unit square set possible for equal parallel diagonals in this basic fashion, with 20 line points, yet there is no highest limit as the pattern continues without end.
The square, one-line-type labyrinths can be generated by using one singular line, aside from the center X and open corner marker, which aren’t required, yet add a completed touch.
Phi significance emerges by increasing the center section and mouth from 2x2 units to 3x3, with a path of 2 units, to form a Bronze Square Labyrinth with near-Phi significance in more than 5 places; with 23 line points, 30 when completed.
There are several ways to actualize Silver and Gold near-Phi significance along the open corner diagonal, however it removes the near-Phi significance at the 3:5 rectangle (A,R,T) shown above, among other places in the Bronze type.
Bronze Significance-
9/6 = 1.5
5/3 = 1.667
8/5 = 1.6
Silver Significance-
13/8 = 1.625
377/233 = 1.61802
Gold Significance-
610/377 = 1.61803
Tale of Tails-
In ancient times, square labyrinths were featured on Greek coins- both a 7 circuit square labyrinth, with the flip side of a man’s head, and a 7 circuit circular labyrinth, opposite a woman’s profile.
Wise Guys Also Tell Tall Tales-
Technically speaking, a square has 4 equal sides, therefore these labyrinths are 'square-ish,' or rather "of square style."
Also, Technically Speaking-
If it's true that, "The only choice in a labyrinth is whether or not to turn back before reaching the conclusion," and there's a dedicated entrance and exit, then one could claim said labyrinth begins at the inscribed circle of the outermost border. Would you agree?
Golden-Section Calipers Measuring Silver Precision:
The Un-Displayed, Yet Calculated Golden Square Labyrinth-
When using whole numbers along the diagonal, as well as a consistent-width path also in whole numbers, then both (A to B to Center) and (B to Center to Far Corner) are actual PHI with a mouth/center of 2,719,598 sq units, and a 14.24 million-unit base. Can you find any smaller numbers to fit the criteria?
Silver moves to gold by also reducing the 17 unit mouth/center to 16.9974875 and adjusting the path width slightly- though not displayed for the simple software used isn’t that precise.
Modern-Day Alchemy-
Can your design software incorporate precision to where the golden ratio is plotted with perfection- possibly exceeding the computer screen resolution, and perhaps even the unaided human visual perception?
Open Submissions-
If so, see the guide below for your submission to be put to golden-section calipers, and possibly featured online. Open to artistic, architectural, and 3D designs as well.
The Bronze Square Labyrinth Measured By The Harmonizer:
Submission Guide:
How accurate can you make the following image? Also, do you spot any other interesting aspects in relation to near-Phi, Phi, Pi, Square Roots, or any other mathematical functions?
Submit designs and comments to GiacomoAureo89@gmail.com