Three Wise Men Labyrinths: Basic, Bronze, Silver, and Gold

May 15, 20224 min read

Updated: Sep 20, 2024

Article By Giacomo Aureo, first published in November, 2021.

Introducing 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 reduces 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 of a woman’s profile. *Some of the coins could be displaying faces of "God heads" and "Goddesses," depending on the belief system / culture.

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 measuring along the diagonal using whole numbers, both (A to B to Center) and (B to Center to Far Corner) are golden to 10 decimal places with a mouth/center diagonal of 2,719,598 units, and a full corner-to-corner length of 14.24 million-units.

The Bronze Square Labyrinth Measured By The Harmonizer:

Modern-Day Alchemy

Can your design software incorporate precision to where the golden ratio is approached with accuracy that exceeds the computer screen (pixel) resolution, and perhaps even the unaided human visual perception? 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 3-D designs.

Also, do you spot any other interesting aspects in relation to near-Phi, Phi, Pi, Square Roots, or any other mathematical sequences or functions?

Submission Guide Symbol

*Note the "approaching" symbol with an arrow inside a circle where the tip isn't touching the circumference. In similar fashion to the purity fineness of precious metals, just how close to the irrational (Q) numbers Phi (upper and lowercase Φ/φ) a Golden Square Labyrinth can be constructed, either on 2-D paper or in 3-D material, is subject to inspection via measurement. For comparison, refined gold is measured in millesimal fineness and karats of purity, where 999.9 parts per thousand is common in commerce, but 100% purity may still be technologically impossible to achieve when refining from alloys. 24-karat gold bars and coins are usually permitted to have a minimum purity of 99.95%, but gold that's 99.9% or higher is still generally considered "pure," and may still sell for the same price as 99.99% gold.

Design Quest / Challenge Questions

How accurate to Phi (Φ/φ) can you make the Golden Square Labyrinth? What accuracy percentage is even possible by hand on paper with a ruler? Can computer software achieve perfection? If not, which program can get the closest to Φ/φ? What levels of precision (to Φ/φ) can engineers and construction crews erect an ~89' x 89' x 55' Pyramidal Labyrinth city-park feature, for 1.) the foundation layout, 2.) the base-to-height ratio (side length to center apex,) and 3.) the heights of points A and B as integer powers of Phi in relation to the center apex?