• 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 = 2*pi/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