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So, while it might be inconvenient for use in proper math, I've really come to love tho 0-360° → 0-1 units on PICO-8 for trig functions (sin, cos).

I've never been sure what to call them, though. They're not degrees, they're not radians, they're not gradians, etc.

I think I came up with a good name.

A "radian" is called that because the angle is expressed as how many radiuses of a unit circle you have to move around that circle's circumference to get to the desired angle. Like, on a circle of any given radius, you have to literally move a distance of 2*pi radiuses around the circle to go a full 360° and end up where you started. A radian is such a distance, but specifically on a circle of radius 1.

So if a radian is an expression of how many radiuses we move around the circle, and PICO-8's units represent how much of the circumference (or how many circumferences) we've moved around the circle, then the unit should be named something to do with the circumference.

"Circumferans" and "circians" don't really work for me. I also considered twopidians, but that's also kinda awkward.

But then, I remembered my discovery of how much better it usually is to use tau in most trig math. Tau, if you don't know, is just another name for 2*pi. One tau is basically one trip around the circle. Tau usually produces cleaner math because it doesn't involve that pesky constant.

(For more on tau, see this classic piece by Vi Hart: https://www.youtube.com/watch?v=jG7vhMMXagQ)

Thus, I propose: taudians

I think it works. Feels okay, it's actually kinda cute, and it's literally a correct way to describe the unit.

Thoughts? :)

( @zep?)

P#49352 2018-02-16 23:49 ( Edited 2018-02-17 20:51)

I think I've been simply calling them "turns" or "revs" (mostly for angular speed, as in rpm - revolutions per minute). but now I'm afraid "twopidians" (better pronounced like "stupidians") is stuck in my brain ;)

also, those have grown on me too, but I'm still having a hard time getting over the inverted sinus. so maybe "retrotwopidians" would be more to the point. (or "stwopidians" for short when I feel grumpy...)

P#49357 2018-02-17 05:52 ( Edited 2018-02-17 11:25)
:: Felice

Yeah, I'd like to call them turns, but it's one of those words that has too many meanings to be used for something precise like an argument description, like:


a - angle, specified in turns

Even though you already know the word "turns", you can't say for sure what that sentence means without extra explanation.

However, if there's a word with that specific meaning, e.g.


a - angle, specified in taudians

You either don't know it and you google it or ask the first time, or you already know from seeing it before, and you know exactly what it means.

That might be why we say "n radians" instead of "n radii"--we don't really need a bespoke word for it, since a radian is a radius, but we have one, because it makes it clear it's a unit.

Plus I like the idea of giving tau more publicity wherever I can. ;)

If not, though... maybe "turnians"? Might be some confusion vs. quaternions.

I'm probably putting too much thought into this. :)

P#49359 2018-02-17 06:31 ( Edited 2018-02-17 11:37)

You could just call them "taus" since each one is tau radians and radian is the standard SI unit.

https://en.wikipedia.org/wiki/Angular_unit#Descriptors has some additional suggestions if you like.

P#49363 2018-02-17 14:00 ( Edited 2018-02-17 19:00)
:: Felice

Well, according to that page, 'turn' is the accepted word for it. Also linked was this specific page:


Can't say I like that as much as something bespoke like taudian or turnian, but if that's the status quo, I'll go with it.

P#49368 2018-02-17 15:51 ( Edited 2018-02-17 20:51)

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