The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art, and the Nude (original) (raw)

2018, The European Legacy

As well as being the simplest catastrophe, the fold is also the most common, the one you are most likely to meet. To introduce the fold, we head to the life drawing class. It may seem unlikely, but the life class is an excellent place to learn catastrophe theory. The purpose of our visit there is twofold. Not only is it a good place to learn the mathematics of curved shape, but in so doing, in unpicking the geometry of the life class, we may learn something more about the act of drawing, about how we perceive the model, and about how we go about representing the body with lines on paper. We may even learn something about the process of perception itself. Let' s start at the very beginning, as they say, with the simplest of all the catastrophes, the fold. It is just a parabola, as sketched to the right. The parabola there has been drawn on its side-it does not matter which way up or which way around you draw it. The point of catastrophe, the turning point, the fold itself, has been highlighted with a dot, and the curves above and below it have been drawn as solid and dotted lines, respectively, to signify that there is usually something different about the two parts of the curve that meet at this special point.