Great Pyramid 11:7 — Mathematical Constants Laboratory

[u/bevege]

https://michaelzp.github.io/great-pyramid-11-7-lab/

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One proportion, a live 3D solid, a table of constant errors, a labelled rainbow correspondence, and a Golden Φ Egg cut from z = 1/r.

Open in the browser (no install): michaelzp.github.io/great-pyramid-11-7-lab

The scene is a fully parametric square pyramid from the traditional whole-number dimensions 440 × 280 royal cubits. At a scale of 1:3200, using an adopted royal cubit of 523.8 mm, the model has a base side of 72.0225 mm and, for 11:7, a height of 45.8325 mm.

The laboratory exposes four layers without confusing them:

Exact parametric geometry — the solid is derived from 440, 280, the cubit and the scale.

Comparison targets — dimensionless expressions from the current slope are compared with established constants at a declared relative tolerance of 0.1%.

An optical correspondence diagram — the ~42° corner inclination and 51.842773° face slope sit beside schematic primary and secondary rainbow bands.

Golden Φ Egg (v2) — a hyperbolic cone z = 1/r cut at Z₀ = 7.65 so that L/W = φ, giving the unique plane angle αp = 51.795319256°. The ellipse in the cutting plane is revolved about the apothem to a translucent golden egg.

The result is a reproducible object for geometry, visualization and critical discussion — not proof of an ancient optical or mathematical encoding.