h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It seems more natural to me to recognise the ratio of a circle's circumference to its *radius*, as a more fundamental constituent of it than twice that. Thus Pi would be c/r (6.283...) Am I missing something?

Surley the ratio of area to radius is a more fundemental one. That said Radians would work better being Pi radians in a circle so you might have a point.

By more fundemental I meant more logical. Clearly they are all as fundemental as each other.

I would have thought the diameter would be first choice because of the ancient problem of squaring the circle, where the base length of the square forms a vital part of the calculation.

B

I would have thought the radius was more fundamental myself, but the Greeks preferred the diameter.

I'm not sure the Greeks actually called the ratio anything in particular. Did they even know the formula for the area of a circle? I suspect the Babylonians first came up with a symbol for the ratio, since they're the most likely candidates for that formula, which only contains Pi, not 2*Pi. Could be wrong though. I don't think Pi was even used until the 17th or 18th century, but again I may be mis-remembering my history.

Given that Euclid's Geometry was more or less the complete and definitive work for thousands of years, I think the Greeks must have known about Pi.

When I say "not even used until the 17th or 18th century" - I mean that the letter Pi wasn't used to represent this ratio until then. Sure, the Greeks definitely knew about the ratio, that's for certain.

Thinking about it you see 2Pi far more often than Pi. Actually I can't think of many occasions (other than Pi r^2 obviously) when you see Pi and not 2*Pi.

The Greeks knew all about Pi, but they didn't call it Pi, they called it the ratio of the circumference to the diameter of a circle. They never had a special symbol for it, since they didn't use symbols. All their mathematics is spelt out in words, making it very difficult to read.

The Greeks knew the formula for the area of a circle, and were the first as far as I know to prove it. They also rigorously proved the volumes and surface areas of a sphere, cone and cylinder, all of which involve Pi, as well as the area under a parabola and other strange curves.

Surely the answer to this can be summed up in one word.

Convention.

Make it double if it keeps you happy. In the meantime the rest of us.......

Wheelwright

Pi is exactly 3

Hexagons make such great wheels, don't they?

I wouldn't have thought so - they have the handicap of existing only on little bits of paper in maths classes.

Oh, what about honeycombs?

Those are six-sided prisms

Is that your way of saying they're fat?

I dunno, a little bit of 3D, and it's insults all the way.

What about benzene molecules?

The structure of graphite?

Neither of those make particularly good wheels, do they?