Euler / Cornu Spiral

The Cornu spiral traces x=∫cos(πt²/2)dt, y=∫sin(πt²/2)dt. Curvature increases linearly — used in road and rail design for smooth transitions.
x = ∫₀ᵗ cos(πs²/2) ds    y = ∫₀ᵗ sin(πs²/2) ds