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It started with that I was thinking of why degrees do not have any dimension, and then I thought of the definition of radians:

q = "angle"

s = "a length on the circles circumference"

r = "radius"

then:

s/r=q

But now we have the dimensions L/L in the equation s/r=q wich then must be dimensionles if degrees is dimensionles. So to solve this problem I need to solve that.

It may have been a stupid question but I want to know, so I appreciate any help.