Tuesday, 11 February 2014
Hanging loose on the Scottish border
It's long time since I did my degree and I've forgotten a lot of the maths. I can remember that when a wire or chain hangs under its own weight, the shape is called a catenary. And I remembered that it involved hyperbolic functions. Like many things in my degree, I could do the questions but didn't really understand. Perhaps I'd better have a look at some of it. Most people have some idea about trigonometry. These are circular functions, based on a circle of radius 1. The equation of such a circle is xsquared + ysquared = 1. A hyperbola is a shape you get for xsquared - ysquared = 1. Instead of sin, you get sinh. Instead of cos you get cosh. Some work to be done here. Incidentally, the photograph is taken in the Kershope Forest and shows a bridge from England to Scotland. I was standing in England and the far side of the Kershope Burn is in Scotland.