Euler Spiral Pillow

Have you ever driven relatively fast in a straight line on a Highway Flyover, and then took an exit ramp that did a 270 degree turn and now you are driving perpendicular to the straight line you were in? The reason you were able to pull this off safely without being tossed out of the window is because Highway Engineers employed what is known as an Euler Spiral to provide an easement curve just before the big turn. Euler Spiral is another one of those beautiful mathematical patterns that is observed in nature. The Euler spiral is a curve whose curvature increases linearly with its length. The solution to the geometry was proposed by Leonhard Euler and Marie Alfred Cornu independently. It is widely applied in Highway and Railroad...