A short anecdotal piece, with a touch of humor.
By Giacomo Aureo, 5-13-2022
When designing the Labyrinths Collection, I became intrigued with the "Hermetic Seal of Light,” however something about it bothered me.
The simplicity of the equilateral triangle, square, and two circles, is appreciated, though it's not centered. Sure it has symmetry, but the circles don’t share a center point. The key 3-4-5 ratios are neat, but I wasn't satisfied enough with the pattern, so I tilted the square, and switched the order.
After adding the shoulder marks came satisfaction: all four shapes share a center, plus the Phi-ratio relationship (inherent wherever a perfect triangle is circled) is accentuated! Also worth pointing out, the circles' diameters are in a 1:2 ratio inner-to-outer, displaying the important double/half pattern.
After adding a labyrinth into the square, the feeling that this design was truly special was legitimate, almost magnetic, maybe even magical. A new concept worth sharing, a contemporary classic! Although at first, a proper name for this design eluded me, I later settled on coining the blank seal the "CentraPHIed Seal of Might," pun intended to blend the definitions of “being mighty,” and “just might be” or “maybe.”
Using a grid system to design the image, the triangle may not be exactly equilateral, yet the grid lines below show the center point in relation to the shapes. It just "might" be centered.
After returning to the seal several times to experiment with labyrinths, wonderment then set in about what next to add into the square. Inspired by studying Cut-The-Knot.com, and noting the square-Phi relationship in connecting a square’s mid-point to an opposing corner, seen here:
...I then included the eight lines and stepped back.
Never before seeing that completed pattern, I wasn’t really sure how it sat with me from a design standpoint. It had symmetry, ratios leading to Phi, and plenty of Fibonacci Sequence number ratios, but that middle 8 (octagon) is rather heavy. So I just left it in the application program and went to sleep.
After waking, to my surprise, a Sacred Geometry e-newsletter had arrived from the website that sells The Proportioner, titled “Next: Geometric Starcut Diagram,” with the 8-lines-in-a-square design I had just completed the previous computer session. There was already a name to the concept, AND it's considered sacred, how cool! Joyful elation: a venerated pattern created without foreknowledge... not that it’s some magnificent feat, but a rather simple image designed with ease.
Happy to learn that mathematicians have studied the pattern in great detail, and delighted to hear the chiming bells of synchronicity, yet slightly unsettled about the name Starcut Diagram. To me, the word "star" is great, though the rest doesn’t really suit my style. Therefore if I were to name it, or re-brand it, I’d stick with word-combining for a fresh, yet familiar sound, something similar to #CentraPHIed. What would you re-name the Starcut Diagram? *Note the comments section for suggestions.
Upon meditation and creative contemplation, a whispered notion "Phi-Cheese" came in from one of the “Feminine Spirits of Truth” who occasionally soars into my auric field of consciousness (she really loves Phi, and apparently kinda likes cheese.) Phi Cheese, what's that supposed to mean? Plus, cheese isn't always fresh...
A few moments later, "aah, a combination of Phi, Chi, and ease, it makes sense!" “Phi,” the twenty-first letter in the Greek alphabet (of 24) signifying the divine mathematical proportion, “Chi” as in the Chinese term for life-force energy that the diagram may emanate / evoke, and “ease” of creation due to its simplicity. Re-brand: The PhiChiEase Square.
Curiously, do you think that Italian guy #LeonaroFibonacci knew about the Chinese concept of Chi? Also, do you think Leo_Fib liked, or loved, cheese? He was Italian, therefore it was practically impossible for him not to like the parmesan-reggiano delicacy. #FibbinNotCheese ;)
Late realizations of near-Phi ratios in the CentraPHIed Seal of Might design are shown below, and the mathematical proofs were expressed by helpful respondents at MathForums.com
Using the GeoGebra App (limited features / free edition) with the measurements set to 10 decimal places, the #CentraPHIedSealOfMight and the #PhiChiEaseSquare are displayed below.
*Notice that the middle octagon of a PhiChiEase Square is not regular because even though each side is the same length, the angles are not all identical.
For those interested, this article by Richard Heath shows how the Starcut Diagram (PhiChiEase Square) can be used to define / display musical tuning. Also, the website GoldenNumber.net exhibits many interesting articles relating to Phi, and is the source of the following image that displays Phi Ratios in the circled perfect triangle. Enjoy the study!
E-mail Comment/Suggestion: The term "Starcut Diagram," coming from Malcolm Stewart’s book Patterns of Eternity, is a star inscribed within a square, and could be referred to as a "SquareStar."
How about renaming the starcut diagram to "Square Phi-Twenty-Five" for the 25 sections it's cut into?