Pi vs Tau Debate

Using tau would uglify euler's equation, wouldn't it?

Does defining tau := 2 * pi make math easier at all?

Still, the discussion is only about convenience. For example, e^ix = cos x + i sin x (with sin/cos taking an argument in radians) would become e^ix = cos 2pi x + i sin 2pi x (with sin/cos taking an argument in turns). It's more cumbersome than the radian-based definitions, but it's not strictly different.

It's not about errors but understanding. A lot of math involving trig is abstract enough to be confusing to most people. Tau makes is [slightly] less so. For example, understanding that sin represents the y value of a point on a unit circle is easier when 1 tau is a full circle rather than 2 pi.

Recently went through this a few times, found it here on HN:http://jackschaedler.github.io/circles-sines-signals/Made me realize how useless degrees are, why pi is used, etc.

What happened to degrees or radians?

Surely you mean pi radians and not pi degrees.

More convenient than degrees. This is unrelated to pi vs tau (using tau or pi doesn't change the meaning of radians, the properties you mention are not affected). What OP is getting at is that the same number of radians, e.g. 1.57 (quarter turn) is more naturally expressed as tau/4 than pi/2.

Personally, I prefer the version with tau (2 times pi) in it rather than the one with pi:e^(i*tau) = 1I won't reproduce https://www.tauday.com/tau-manifesto here, but I'll just mention one part of it. I very much prefer doing radian math using tau rather than pi: tau/4 radians is just one-fourth of a "turn", one-fourth of the way around the circle, i.e. 90°. Which is a l

For anyone that finds it beautiful isn't there a bit of humanisation and definition involved (for example the Sine function used in deriviation uses 'pi' instead of 90 degrees), not to mention Sine is a human created function. You could have e to pi (90 * -1) too.. or a different method to define angles instead of having 360 degrees (base 60)