41–43 of 43 posts
Earlier quoted context omitted.
Telling a 3rd grader to think of it like an integral seems to be putting the cart WAAAAAAAY before the horse. Edit: Also that's is hardly a more fundamental equation because you could also say e^(1024 pi * i) = e^(4096 * tau * i) = 1.
It won't amaze third graders, but it would make a lot more sense the first time you learn integral calculus
Earlier quoted context omitted.
51° is the latitude of the city I'm living in, and I chose 1/7 τ because it comes pretty close. I could have used 0.14 τ to make my point as well: If you want to avoid fractions in common cases, you'll need to multiply with an arbitrary number like, say 100 (which has obvious benefits in a base-10 system), but arguments could be made for something like 400 (in which case we end up with gon) or, say 360, which has the…
> 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 pr…
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.
Earlier quoted context omitted.
> 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 pr…
A 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.
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.