Originally Posted by Anarion
So, I've seen this before, and I still think the simple argument that avoiding fractions wherever possible beats out tau for ease of learning. 2pi is much easier to work with than tau/2 because that little bar is going to intimidate children across the world when they need to find the areas of circles.
1. So ... you want to confuse them a hundred times more when they get to radians and trigonometry and all the other stuff where tau really shines and makes everything so much neater? Wouldn't it be better to accept a tiny bit of possible confusion in one area to eliminate a much bigger and more pervasive confusion elsewhere?
2. Getting a good grip on division is something I'd say is important for kids at that age. If they are scared by having to halve
something when they get to circles and areas, then their education has failed them massively! If we were talking about stranger fractions rather than simply halving stuff, then maybe
. If squaring something is not scary, then division by 2 should not be.
If children are intimidated by simple fractions, it is not the fault of the fractions (or the children), but of their teachers, parents, educational system and/or society as a whole.
3. You could write it as 2A=tau * r^2 if you really wanted to avoid obvious fractions. Perhaps there's even an opportunity for some lesson or (possibly visual) aid to help them better understanding the formula or division itself. As a teacher I'd probably see an opportunity for some discussion here.