Whilst trying to work out areas of circles for my DIY Vulcan bomber project (See link (or not( suit yourself)))...I got bored of this pi times the wotsit squared.

Having a ponder....I thought a circle with a diameter of 1 [insert units of length of your choice] would have a certain area, now, if
we were to draw a square which has the same length sides it'll have an area of 1 [units] Obviously the circle is a bit smaller. In fact the circle will be roughly 0.785398175 of the area of the square

So, instead of all this faffing about with radius's and pi, we can just measure the diameter, multiply it 0.785398175 and you'll get a close-ish answer.

Tauhttp://tauday.com/ If you don't like pi, try tau. Though it actually makes calculating the area of a circle slightly harder. [scad mientist, Aug 08 2011]

erm, did just try it on circles of radius of 1, 2, 2.5 and 3, so it does hold for most circles.

Actually, I got bored two weeks ago ran the idea past one of my students who's a post-grad in maths and he wrote up the proof of it.

To me, finding the diameter, squaring it and multiplying by 0.785 is a lot easier. It's mighty easy to me to work out squares but more tricky to work out (on paper) what the square root of anything is, as it seems to involve kind of ranging shots and then adjusting the figure being used.

There's also the fact that pi shows up in all sorts of formulae completely unrelated to circles. It's a universal constant, not just for round things, and is therefore much more useful to learn.