This one is probably of most interest to Othko; Pentagathus need read no further.
I ran into the Tau Manifesto (http://www.tauday.com/tau-manifesto) today. It's an extended argument for the proposal that we should use a 'circle constant' of τ (tau) = circumference/radius, rather than the familiar π. τ = 2π, of course. I think it's quite well thought-out, though I suspect I won't switch simply because I'm too used to π-based formulae now.
This is one of those issues I'm quite impartial on. The Tau manifesto makes some very good points, and it does make so much teaching of the subject simpler, as the fractions make more sense. However from a practical point switching our entire education system to teach tau rather than pi would be difficult, as there would be people floating around unsure on definitions and such. Furthermore Tau is not as famous as Pi, so kids would be learning about tau with a different attitude to how they learn about pi. To be honest I believe the best solution would be to go back in time and get the definition changed at the root of the problem. That said, considering tau really helped me to learn stuff about sines, cosines, tangents, radians etc by making things simpler.
Othko: I'm interested that you got to know about tau - were you actually taught about it, or did you find out from your own reading? Your comments certainly reinforce the point in the manifest about it making learning easier.
I think I found a link on reddit at some point, or watched vihart's video on the topic, and read the manifesto. Yeah, it made it much easier to learn, especially radians, as it makes more intuitive sense (in physics I convert to tau mentally to figure out path lengths in wavelength/period. Obviously this is just a factor of two, but I think in terms of tau rather than pi, if that makes sense.) I've never heard it mentioned in an actual lesson though, which is something of a shame, as I think the concept is pretty helpful.
Just had a look in to this because of you guys and it looks like it would be really helpful with my trig, it makes things a lot more simple. I think I might try to convert my friends. :P
Excellent! I'm glad it's been helpful.
Well, it may by simpler and easier to use, but I have absolutely no problems understanding and using pi, so why change?
This is a point most people make, and I don't really think there is an appropriate response. While it does make things simpler, it is only a factor of 2, so it's not too taxing. However surely we want mathematics to be as simple and elegant as possible, without one of the fundamental constants requiring multiplication by two. There is also the point of future generations, who will likely pick up radians and trig using tau much easier than with pi, making maths (and related subjects) less daunting.
Some videos on the topic:
Spoiler