The Euler spiral

Students of literature read Shakespeare; students of music listen to Bach. In mathematics such a tradition is, if not entirely absent, at least fairly uncommon. This book is meant to address that situation. Although it is not intended as a history of the calculus, I have come to regard it as a gallery of the calculus. - (William Dunham)

I am reading Dunham's book. Calculus Gallery. While reading I realized that I couldn't do the integral $$\int \cos{(x^2)}\ dx ,$$ anyway to make a long story short I discovered yet another beautiful curve ( most beautiful ever? maybe ): the Euler spiral, it is parametric plot of two Fresner integrals.

An Euler spiral has the property that its curvature at any point is proportional to the distance along the spiral, measured from the origin.

Exercise ( read: question ) How can we rotate the spiral?

Peek preview of Dunham's book.