3 ms·
> Actual radians (ie not expressed as fractions of 2π) I think this is the source of your problem: you view an expression like "τ/8" or "π/4" as less an "actua
by blahedo 14y ago
> Actual radians (ie not expressed as fractions of 2π)
I think this is the source of your problem: you view an expression like "τ/8" or "π/4" as less an "actual" radian measure than the inexact ".785". That's a function of how a lot of us were taught math, I think, and I'm quite sure that it's only made worse by the fact that the use of π camouflages the fact that this is related to fractions of a circle. But your premise is faulty. Of course radians expressed in decimal are user-unfriendly, but radians expressed in decimal are no less "actual" than radians expressed as fractions of τ or π.
- cygx 14y agoA physical quantity is given by numerical value and unit of measurement. Giving angles as fractions of τ changes the unit of measurement from radians to turn. There are applications for which neither radians nor turn are a good fit. Similarly, oftentimes the 'messy' SI units are a far better fit than any 'more fundamental' system of natural units.
- oelewapperke 14y agoThat's true to a degree. But when you think about it, there does not exist any physical quantity that can be specified as an irrational number (because every measurement is quantized, so you could argue even a whole number. Rational numbers and whole numbers are models of eachother however, so there is arguably no "fundamental" difference). As to why people can calculate better/easier with relatively low numbers compared to irrational fractions ... does that really need explaining ? How much is 1+1 vs how much is 1/7 tau + 1/3 tau. Degrees are very useful and quick indeed.