Why are curves sexy?

They just are.

That probably is not the most conclusive answer and in fact, that might even be called a flippant answer. 

But it is a challenging question and the precise answer depends on context. If we take a mathematical approach, we can say that curves cannot be defined by two points or it could be defined as a straight line deformation. In the natural world, we are surrounded by curves and examples in the real world are nearly overwhelming.

Curves are aseptically pleasing to the human brain.  There is a natural grace to a curve and that somehow provides a mental reassurance.  Maybe it has some kind of pre-natal/maternal basis.

So, back to the first comment; they just are.

Locals will recognize this as looking north on Wisconsin State Highway 35, halfway between Stockholm, Wisconsin and Maiden Rock, Wisconsin.  The bluff is called Maiden Rock and this photo was taken about 30 minutes before sunset, thus the bluff face illumination. My partner-in-crime was the driver of the vehicle and the entire photo was staged, right down to the brake lights.

The top of Maiden Rock bluff is a land trust and there are public paths that you can take right out to the bluff edge.  Look for those photos later.