Eon wrote:It is stated that some formulas are simpler to write when using pi, but really does this matter? Is the end goal trying to minimize the amount of ink you need to print something?

To me a more valid argument is whether or not it is simpler to "see". To think about. To grasp. Tau radians per revolution makes sense. You can add integer multiples of tau to an angle to still mean the same angle. Nice and simple.

I agree completely, except that I call this definition natural and usually distinguish between being more simple and being more natural. Then I notice that whenever tau is simpler, it is also more natural, but when pi is simpler, tau is still more natural.

Eon wrote:But ultimately why do we need to choose? Can't people use the one they are comfortable with? If I had to fight for something in mathematics it is this:

How can the definition of sin^n(x) suddenly change when n = -1? It is then said to mean arcsin instead of [sin(x)]^(-1) like with other values of n, in particular 2.

Thank you! I hate this notation and was confused by it for a while. I often point it out as an example of other terrible notation to refute claims that pi is okay just because it's been used for a long time. I always write arcsin x instead of sin^-1 x to avoid using this counterintuitive notation, although that doesn't really fix it. What should be changed is that f(x)^2 should always be written that way, not as f^2(x). That way, f^-1(x) can mean the inverse of x without any confusion as to whether it means the inverse or an exponent. Another way to fix the problem would be to use something like f*(x) to mean the inverse of f(x) rather than using f^-1(x).