## Rule of twelfths

The rule of twelfths is a memorable way to approximate a sinusoidal curve by twelve equally-spaced line segments of slope

¹⁄₁₂, ²⁄₁₂, ³⁄₁₂, ³⁄₁₂, ²⁄₁₂, ¹⁄₁₂, ⁻¹⁄₁₂, ⁻²⁄₁₂, ⁻³⁄₁₂, ⁻³⁄₁₂, ⁻²⁄₁₂, and ⁻¹⁄₁₂

respectively. It rounds $\frac{\sqrt{3}}{2} \approx \frac{5}{6}$ but otherwise uses exact values along the curve.