[NoraSpinnor]

Here’s a fast, practical on-ramp to five “core constants” you’ll spot in everything from architecture to card spreads.

φ (phi, the golden ratio, ≈ 1.618):
Phi is the number for which the whole relates to the larger part as the larger part relates to the smaller. You see it in pentagons and pentagrams, and the ratios of consecutive terms in additive series (…55, 89, 144, 233…) converge toward it. In nature it appears in spiral counts of plants and shells; in design it yields balanced rectangles and spirals; in divination a φ-based spiral or five-point layout is a clean way to read for growth, timing, and integration.

√2 (≈1.414) is the diagonal-to-side ratio of a square. It’s the backbone of the A-series paper standard—fold any sheet in half and the aspect stays √2. Geometrically it’s the 45°–45°–90° triangle; practically it’s perfect for progressive scaling that preserves proportion.

√3 (≈1.732) governs the equilateral triangle and the vesica piscis (the lens formed by two overlapping equal circles). It sits behind sixfold and hexagonal patterns—think honeycomb and snowflakes—and the 30°–60°–90° triangle. Designers use it for hex grids and balanced tilings; ritual workers use vesica forms as “birth” or threshold windows.

√5 (≈2.236) is the diagonal of a 2×1 rectangle and the algebraic heart of φ, since φ = (1+√5)/2. It underlies pentagonal geometry and the “root rectangle” constructions that let you step sizes accurately without a ruler. When you want golden relationships but you’re drafting by hand, constructing φ via √5 is dependable.

Finally, π (pi, ≈3.14159) is the ratio of a circle’s circumference to its diameter and shows up in everything cyclical: circles, orbits, ripples, drums, breathing, and heartbeats. Designers lean on circular and radial symmetry for wholeness and fairness; practitioners cast circles, lay out zodiac wheels, or build ring spreads.

To use all of this fast: pick the ratio that matches the energy—φ for growth, √2 for clarity, √3 for alignment, √5 for agency, π for cycles—then lay cards or place objects using those shapes and spacings.
Do you use any of these proportions?
Share your thoughts and experiences.

[LisaPhan]

Have only heard of the golden ratio and pi. You mentioned the others and I can see how those are important too they show up a lot.

[Author]

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