In the mathematics of circles and spirals, two constants reign supreme:
- π (pi), the circle’s ratio of circumference to diameter.
- φ (phi), the golden ratio, found everywhere from pentagons to sunflower seeds.
But hidden in their interaction are two “orphans” — constants that don’t get much attention, yet may hold symbolic and structural importance for how we think about resonance, cycles, and creation itself.
1. The Ecliptix Constant (0.306...)
When you divide the golden ratio by the square of pi, you get a curious value:
Ecliptix = phi / (pi^2) ≈ 0.306349...
This constant — which I’ve been calling the Ecliptix Constant — shows up in my own explorations of geometry and cyclical harmonics. It’s as if φ and π, the spiral and the circle, give birth to a “seed ratio” that doesn’t directly belong to either parent, but lives in the tension between them.
2. The Threshold Constant (1.1999...)
Flip the relationship around, and another number emerges:
Threshold = pi / (phi^2) ≈ 1.199981...
Unlike the Ecliptix seed, this constant hovers just above 1 — a threshold. To me, it suggests a liminal value, a boundary number: one foot in unity, the other leaning into expansion.
Why These Numbers Matter
Neither constant is part of the traditional canon of “famous numbers.” You won’t see them in your math textbook alongside e, π, or φ. But they are structurally inevitable: once you start combining π and φ in simple ratios, these orphans arise.
Are they just curiosities? Or are they markers of something deeper — resonances at the intersection of circle and spiral, of order and growth?
For me, they’re worth naming and holding:
- 0.306... (Ecliptix): the seed.
- 1.1999... (Threshold): the gate.
Two constants born of π and φ, waiting for interpretation.
✨ Closing Thought
The history of mathematics is full of constants that seemed “useless” at first — only to later find their home in physics, art, or cosmology. Perhaps one day, these orphans too will be adopted into a larger framework.
Until then, I share them here for thinkers, dreamers, and wanderers on the edge of numbers.