3 ms·

51° is not 1/7 τ. 1/7 τ is (51 3/7)°, or 51.428571...°. If you round that to 51°, then presumably you're doing something where inexact numbers are fine, in wh

51° is not 1/7 τ. 1/7 τ is (51 3/7)°, or 51.428571...°. If you round that to 51°, then presumably you're doing something where inexact numbers are fine, in which case you might then use "0.89 (radians)". My intuition is better for degrees here, but I think that would change if I spent ten minutes doing calculations involving real radian measures.

cygx 14y ago
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 benefit that it's the established standard (even though it's not the most obvious choice). Actual radians (ie not expressed as fractions of 2π) are pretty user-unfriendly in a base-10 system.
- 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 ago
    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.
    - oelewapperke 14y ago
      That'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.

cygx 14y ago

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 benefit that it's the established standard (even though it's not the most obvious choice). Actual radians (ie not expressed as fractions of 2π) are pretty user-unfriendly in a base-10 system.

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 ago
  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.
  - oelewapperke 14y ago
    That'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.