Sacred Geometry — Art & Science
A compact, searchable guide to classic ratios, key ideas, and interactive compass-and-straightedge diagrams — plus a 3D wireframe viewer of the Platonic solids.
Curtision.com
TL;DR
- Start from first principles: point → circle → two circles → vesica piscis.
- Root rectangles: √2, √3, √5 families used in proportioning systems.
- Golden ratio (φ ≈ 1.618) appears in composition and proportional division.
- Metrology: discussions of how units and buildings relate through proportion.
- Includes interactive construction diagrams and a 3D wireframe solid viewer.
Key numbers & ratios
| Value | Name / context | Use |
|---|---|---|
| √2 | Diagonal of a square | Root-2 rectangle |
| √3 | Equilateral / vesica geometry | Root-3 rectangle |
| √5 | Diagonal construction | Golden rectangle method |
| φ | Golden ratio | Proportion / division |
| 25,920 | “Great year” number (precession framing) | Cycle mapping |
| 72 | Years per degree (25,920/360) | Angle→time mapping |
Metrology
Measurement traditions often connect geometry with practical building and surveying.
Royal cubit & remen (√2 relationship)
Some presentations compare example values (royal cubit ≈ 20.6265 inches, remen ≈ 14.58 inches) where the ratio is close to √2.
Celestial geometry
Precession of the equinoxes
- Precession is the slow shift of Earth’s axis relative to the fixed stars.
- Some traditions use 25,920 as a rounded great cycle number.
- From that: 72 years per degree is a common conversion.
Key figures
- St. Augustine
- Galileo
- Johannes Kepler
- Plato
- Pythagoras
- Protagoras
- Alexander Thom, John Michell
Notable quotes
“Numbers are the thoughts of God.”
“Mathematics is the alphabet with which God has written the universe.”
“Geometry existed before the creation. It is co-eternal with the mind of God.”
“Man is the measure of all things.”
Core ideas
Circle & square
Often used as a contrast between unity/infinity (circle) and measure/structure (square).
Vesica piscis
The overlap of two equal circles (center separation = radius) is used as a generative seed for many constructions.
Geometric constructions — interactive demos
Use the sliders to step through each construction.
1) Vesica piscis
2) Root rectangle ladder
3) Golden rectangle
3D wireframe viewer — Platonic solids
Drag to rotate, scroll to zoom.
Architecture & sites
- Stonehenge
- Great Pyramid of Khufu
- Parthenon
- Angkor Wat
- Chartres Cathedral
Glossary
Vesica Piscis
Overlap formed by two equal circles whose centers are one radius apart.
Root Rectangles
Rectangle family with ratios √1, √2, √3, √4, √5…
Golden Ratio (φ)
φ ≈ 1.618… line division where whole/large = large/small.
Metrology
Science of measurement (units, standards, relationships).
Gallery
