3 ms·
I actually (embarrassingly) got tripped up by that a bit. So, you're saying that radians/degrees _are_ a unit because we can use them to describe a count of so
by ShamelessC 6y ago
I actually (embarrassingly) got tripped up by that a bit.
So, you're saying that radians/degrees _are_ a unit because we can use them to describe a count of something, but they're still in fact dimensionless?
Is that because 2*pi or degrees never refer to an actual physical length? I think that's what trips me up because I generally have thought of degrees and radians as essentially units of length around a circle. But I suppose that since we're working with circles of arbitrary rather than specified diameter, they're still unitless.
I think I got to it on my own at the end there ha but I'm happy to be corrected!
- SAI_Peregrinus 6y agoCorrect, the arbitrary length is the reason they're dimensionless. A singular mathematical point can still rotate, but the arc length will always be zero.
- klyrs 6y agoOne way to think about radians is "feet (of perimeter) per feet (of radius)" -- the dimensional units cancel and you're left with a dimensionless unit. Taxes are a familiar dimensionless unit -- dollar owed to the government, per dollar spent on snacks. The dollars cancel and you're left with a raw percentage. (actually, to convert to a percentage you multiply by 100 percent per whole; another dimensionless conversion)
- quantified 6y agoIf they are truly dimensionless, when is it meaningful to multiply a non-currency value by them? There’s still a semantic that attaches the rate to dollars obtained in a transaction.