Personally, I prefer the version with tau (2 times pi) in it rather than the one with pi:

e^(i*tau) = 1

I 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 lot easier to remember than pi/2, and would have made high-school trig so much easier for me. (I never had trouble with radians, and even so I would have had a much easier time grasping them had I been taught them using tau rather than pi as the key value).

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kqr 44 minutes ago | parent | next [-]

The one place where radians are more convenient is when you are at the centre of the circle. Then something which is as wide (or tall) as it is far away subtends one radian in your view. (And correspondingly, if it subtends half a radian it is half as wide as it is far away, etc.)

This happens to be the most common situation in which I measure angles.

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snthpy 4 hours ago | parent | prev | next [-]

This!

I've been posting the manifesto to friends and colleagues every tau day for the past ten years. Let's keep chipping away at it and eventually we won't obfuscate radians for our kids anymore.

Friends don't let friends use pi!

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rmunn 3 hours ago | parent | next [-]

Oh, pi has its place: in engineering, for example, it's much easier to measure the diameter of a pipe than its radius: just put calipers around the widest point (outside or inside depending) and you have the diameter. In fact, you probably wouldn't ever measure the radius; in places where you need the radius, you'd just measure the diameter and divide by 2.

But for teaching trig? Explaining radians should definitely be tau-based.

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avmich 4 hours ago | parent | prev [-]

I wonder how many places we have in modern math symbols which we use for historical reasons, rather than because it's most convenient overall. I guess we are balancing things here.

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yen223 4 hours ago | parent [-]

Arguably, base-10 counting vs base-12 counting is one such example

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snthpy 2 hours ago | parent | next [-]

Which one of those is preferable? It seems to me that they are both historically based. 10 x 10 is also 100 in base-12 (it's only in base-10 that it looks like 144).

IMHO, in a modern setting base-16 would be the most convenient. Then I maybe wouldn't struggle to remember that the CIDR range C0.A8.0.0/18 (192.168.0.0/24) consists of 10 (16) blocks of size 10 (16).

	▲	Sharlin 7 minutes ago \| parent [-]
		There’s nothing particularly convenient about base-ten; for real-world uses base-twelve would be preferable thanks to its large number of divisors (and even larger number of divisors of its multiples like 60). Which is exactly why 12 and 60 historically appear in many contexts. A number theorist would probably want a prime base, so that N (mod 10) would be a field. A power-of-two base wouldn’t be particularly convenient to anyone except a small minority consisting mostly of hardware and software engineers.

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3 hours ago | parent | prev [-]

[deleted]

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paulfharrison 42 minutes ago | parent | prev | next [-]

535.491…^i = 1

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badlibrarian 5 hours ago | parent | prev | next [-]

Which would be e^(i*tau) - 1 = 0 if you wanted to honor the spirit of the Identity.

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zkmon 3 hours ago | parent | prev | next [-]

Though the argument is technically correct, it is unnecessary at this point of time. Same as renaming cities and countries to "correct" history.

	▲	throwawayk7h 3 hours ago \| parent \| next [-]
		Disagree. This is not so much about epistemological correctness as it is about what's useful and convenient. math.tau is an easier and more intuitive constant to work with.
	▲	setopt 3 hours ago \| parent \| prev [-]
		Math didactics is all about making math more digestible for the next generation, even if it breaks with history. For now, I’ve just explicitly written exp(2πiν) etc instead of exp(iπν) in my work; explicitly writing out 2π and treating it as effectively one symbol does have similar conceptual benefits as working with τ.

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karmakurtisaani an hour ago | parent | prev [-]

Ah, one of these battles that are very hard to fight to gain essentially nothing.