math:geometry
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Table of Contents
Polygons
Regular Polygons
- polygons inscribed within a circle of radius R with equal side length s
- each side also spans an arc of angle Θ
- we can easily calculate the side s via General Pythagorean
- c2 = a2 + b2 - 2ab * cos(Θ) where c is the side opposite Θ
Pentagon
- Θ = 360/5 = 72 degrees (2π/5 radians)
- s = √(R2 + R2 - 2R2 * cos(72-deg))
- = √(R2 * (2 - 2 * cos(72-deg)))
- = R * √(2 - 2 * cos(72-deg))
- ≅ R * 1.17557
Hexagon
- Θ = 360/6 = 60 degrees
- s = √(R2 + R2 - 2R2 * cos(60-deg))
- = √(2 * R2 - 2R2 * 0.5)
- = √(2 * R2 - R2)
- = √(R2)
- = R
math/geometry.1764624590.txt.gz · Last modified: 2025/12/01 21:29 by ron