Friday, July 27, 2007

Two pi or not two pi?

Hmm... this is interesting, though it's been linked to by others far earlier than me. Basically the author points out that way back when it was decided to define pi as being 3.14..., we would have been much better off defining it as 6.28..., that is to say, two times our value of pi. Apparently a lot of formulae would work out looking a whole lot neater if we did, and radian measure would be much easier: 360 degrees would be pi radians (whole circle = all of the pie!); 180 degrees would be pi/2 (half circle) etc... I can see the attraction. Though it wouldn't clear up the misconception that many students have, when they suddenly decide that pi equals 180 in the middle of an integration question involving trigonometry.

Of course the actual definition of pi as a ratio would need tweaking, but that would be easy enough.

Oh well... missed opportunities, eh?


maths teacher said...

Credit where it's due, this link came from the rather excellent "gooseania" blog... I've added the blog as a link on the right hand side of the page, as it's well worth reading.

Antony F Heaton said...

I would love to read it: I have long believed that mathematicians should use "two pi" as the basic constant, ever since I was introduced to the formula linking the fundamental constants e^(i*pi) = -1. The -1 worried me until I realised that the pi that everyone uses is the wrong constant.

Pity I cannot get in, as it is a closed blog.