Pi anyone?

piIt suddenly occurred to me while looking elsewhere that while we can be precise about the area of a square, we can’t be precise about the area of a circle. The reason, of course, is that we can not be precise about Pi. (At least I don’t think we can – doesn’t it just run on in a random string ad nauseum?)

This seems to say something significant about the very nature of a circle and it brought me back to a quarter of a century ago when I was playing with – and writing about – the computer language, Logo. AT that time I wrote a simple, recursive routine that drew a triangle, then a square, then a pentagon, hexagon, etc. Eventually the figure on the screen had so many sides any practical person would call it a circle. And that was a revelation to me because I then understood that a circle was simply another polygon, but with a heck of a lot of sides.

Now, 25 years later, I see how Pi fits into that concept, for the circle never becomes perfect and so pi – the ratio between the radius and the circumference – can never be defined.

I think?