Sacred Geometry & Spatial Proportions
Interactive mathematical solvers for the Golden Ratio ($\Phi \approx 1.618$), display aspect ratios, and Pythagorean right triangle theorem with real-time SVG diagrams.
Golden Ratio (Φ)
Harmonic Scales & PartitionsAspect Ratio
16:9, 4:3, 1:1, 9:16 & 21:9Pythagoras Theorem
Interactive SVG SolverGolden Ratio (Divine Proportion) Calculator
Euclidean Extreme & Mean Ratio Composition Solver (φ = 1.6180339887...)
Expanded proportion for hero containers, sidebar ratios, and major grid columns.
Condensed proportion for secondary sidebars, captions, and harmonious padding.
Golden Section Geometric Partition (1 : 1.618)
Total: 1000 px5-Step Golden Ratio Modular Scale
r = φ^n| Harmonic Step | Formula | Calculated Size | Recommended Usage |
|---|---|---|---|
| Step -2 (b / φ²) | Step | 381.97 px | Sub-caption / Micro-tag |
| Step -1 (b / φ) | Step | 618.03 px | Small text / Caption |
| Base (b) | 1.000 × b | 1000.00 px | Body Text / Baseline |
| Step +1 (b · φ) | Step | 1618.03 px | Heading H2 / Subtitle |
| Step +2 (b · φ²) | Step | 2618.03 px | Hero Title H1 / Display |
skymotion20-20).Recommended Euclidean Geometry & Proportion Texts
Hand-selected peer-reviewed literature, optical instruments, and mechanics resources verified by physics educator Traian Anghel.
The Golden Ratio: The Story of Phi
By astrophysicist Mario Livio. The definitive exploration of the divine proportion in art, nature, and cosmology.
Sacred Geometry: Philosophy and Practice
By Robert Lawlor. Pythagorean harmony, Euclidean proportioning, and geometric harmonics.
Quadrivium: Number, Geometry, Music, & Cosmology
The four classical liberal arts combining Euclidean geometry, harmonic intervals, and sacred proportions.
Display & Media Aspect Ratio Dimension Calculator
Digital Screen, Sensor & Video Composition Proportions (SMPTE & ISO)
Pythagorean Theorem & Right-Angled Triangle Solver
Euclidean Geometry Fundamental Relationship (Euclid Elements Book I, Prop 47)
skymotion20-20).Recommended Euclidean Geometry & Proportion Texts
Hand-selected peer-reviewed literature, optical instruments, and mechanics resources verified by physics educator Traian Anghel.
The Golden Ratio: The Story of Phi
By astrophysicist Mario Livio. The definitive exploration of the divine proportion in art, nature, and cosmology.
Sacred Geometry: Philosophy and Practice
By Robert Lawlor. Pythagorean harmony, Euclidean proportioning, and geometric harmonics.
Quadrivium: Number, Geometry, Music, & Cosmology
The four classical liberal arts combining Euclidean geometry, harmonic intervals, and sacred proportions.
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