Having made an abortive attempt to get a degree in mechanical engineering, I did get far enough advanced in pure mathematics to be able to appreciate how beautiful some of it can be, even if—or perhaps especially if—you don't quite understand much of what's going on.
For example, I remember how awed I was—silent, upon a peak in Darien, you might say—when I was shown one of the ways of calculating the area of a circle using calculus. At that time I did have a hazy notion of what calculus was about; it's all gone, of course, and nowadays I couldn't tell the difference between an integral coefficient and a packet of soda mints.
No great disgrace in this. Ever since the Rhind papyrus, thought to be based on a document dating from 1800 BC, the greatest minds have wrestled with these concepts. Archimedes and others had a shot at squaring the circle, but it took Newton or maybe Leibnitz to make calculus really useful.
Anyway, never mind about that. What I do remember is that the particular method of finding the area of a circle that I was shown consisted of only a few lines of ineffable elegance. It went like this:
You take a slice across the circle, of thickness x and width y. Then, and this is the bit which will cause anyone who knows any serious mathematics to fall about with uncontrollable laughter, you can say that the area of the strip is d(x) times d(y) and when d(x) tends to zero and d(y) is twice the radius of the circle then the area of the circle is obtained by giving the whole thing a thorough differentiation and then integrating between the limits of something or other. The answer, as everybody knows, then works out as πr(squared). (How do you do superscript in Blogger?)
All the above is of course meaningless gibberish, but it should give enough of a hint to enable someone with a bit of maths (or math) to identify the particular method that I so vaguely remember and then to spell out the few elegant lines which have swum out of my ken.
If there is a Senior Wrangler out there who can remind me of them then I shall be happy to reward him for his trouble by sending a cheque for twenty pounds sterling to the Save the Children Fund.
[Oh no, I see that the last Senior Wrangler, who was admitted a hundred years ago, died in 1946, so he won't be much help. Anyone else, then?]