spirals

The above spiral is the Euler spiral (also called the Cornu spiral, or clothoid). The curvature of the Euler spiral increases linearly, from infinitely negative (which corresponds to curving to the right) in the bottom left, to infinitely positive (curving to the left) in the top right. In the middle, it thus has a curvature of zero (like a straight line). Of course, I have only drawn a segment of the spiral, hence the open spaces at the beginning and end.