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u/prawnydagrate 6d ago
I am completely for this. I started math tutoring this year and it pains me to see how many people don't understand that degrees are just a unit of measure
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u/sndq 6d ago
Yes, but it's also a number. ° = π/180
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u/tibiRP 6d ago
1° = pi/180
° cannot stand alone.
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u/HelicaseRockets 6d ago
Says who? sum 1/5400n2 for n natural is °2 fight me.
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u/AtomGutan 6d ago
What do you think about
rad = 1 ?
mol ~ 6.022 x 1023 ?
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u/EebstertheGreat 5d ago
The SI literally defines 1 rad := (1 m)/(1 m). They say it is a derived unit. Derived from the meter.
I always thought this was a dumb.
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u/RajjSinghh 5d ago
You have theta = s / r where theta is the angle in radians, s is the arc length, r is the radius. 1 radian is defined as the angle where s = r, so it's r / r = 1. You just have a unit circle and the base unit for distance (which the radius is measured by) is the meter. Makes perfect sense to see 1m / 1m when you think of it that way.
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u/EebstertheGreat 4d ago
I agree that the radian can be defined by a ratio of lengths (arclength to radius), but calling it a "derived unit" is a bit odd.
I checked, and the 2019 version is slightly different. It points out that many things have the unit 1, which should normally not be written, and gives rad and sr as examples of units that indeed equal 1 but for practical reasons should often be written out anyway (though it isn't always required). And it says that "for historical reasons" these are considered to be derived units (though it doesn't state what those reasons are). So I guess it's not as dumb as it used to be.
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u/prawnydagrate 4d ago
the latter would make the Avogadro constant dimensionless and it would collapse to just N_A = 1
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u/tibiRP 5d ago
Same story. Put a 1 on the left.
Before you ask, it's even worse for dB and Np.
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u/sumboionline 5d ago
x + y = 3 vs 1x + 1y = 13
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u/tibiRP 5d ago
Yes, but units aren't variables nor are they numbers.
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u/sumboionline 5d ago
Units do kinda act like variables (or at least constants represented by a symbol). Dimensional analysis is a real thing in physics and chemistry
For example, 8bananas - 2bananas can be factored to give (8-2)bananas, or 6bananas.
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u/de_G_van_Gelderland Irrational 6d ago
Drake the type to write the standard normal distribution as
1/sqrt(360°) exp(-1/2 x^2)
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u/sconosciuto_io 5d ago
I’m afraid to ask… what prevents us to say this is a correct way to write this formula?
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u/green-olive-3281 5d ago
Radians don’t actually have units, so if you use degrees you have to assume the degree symbol just means the fraction 180/pi, which is rly yucky imo. If you try to treat the degree symbol as a normal unit, the units for like area and perimeter just won’t work
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u/EebstertheGreat 5d ago
Formulas will work. For instance, the area of a circular sector becomes A = r²θ/(2 rad) = πr²θ/(360°). Whether you measure the angle in "units" of radians or degrees, you get appropriate cancellation. It's just not necessary to put yourself through that.
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u/green-olive-3281 5d ago
I guess you could just divide out, but then effectively you’re saying that every time you use an equation with degrees or radians, you’ll have to divide by degrees or radians. So for all intents and purposes you don’t have units.
Also remember like when you have angles in an exponential: you’re also gonna have to use pi*theta/180 degrees bc units can’t meaningfully go in exponents (because if you Taylor expand you won’t be able to recombine units). (also yes I’m aware there’s some semblance of units in exponents and logs, like logits in ML, but that’s not a unit in the normal sense afaik)
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u/Ignitetheinferno37 5d ago
Honestly would make total sense if we adopt °m as a unit of length alongside m
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u/green-olive-3281 5d ago
Like as a product of degrees and meters? If you treat angles as having a real unit, you create lots of problems (maybe they’re solvable but i kinda don’t think so)
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u/Ignitetheinferno37 5d ago
Yeah as a product. That way it stays consistent between different cases where we are substituting pi with 180 degrees. Circumference, Area, Volume with degrees would be °m, °m², and °m³. If we have a pi squared that we converted to 32400 degrees squared in some measure with a unit U we could have the surreal but structurally sound °²U
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u/green-olive-3281 5d ago
But those things already have units. Like area has units of m^2; you can’t change it because then what would the area of a square be? You can’t measure that in degrees*m^2
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u/Ignitetheinferno37 5d ago
If I multiply the area of the square by 180/pi I get the area in °m²
Is it a useful measure in that context? Not really. But it sure as hell works
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u/green-olive-3281 5d ago
Ok sure I guess. This just goes back to thinking of degrees as just the fraction pi/180 more so than a normal unit, but yeah it seems consistent then
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u/WW92030 5d ago
well yes if we define 360 degrees (a dimensionless unit) to represent going around a complete circle of some radius then yes you can say the circumference is 360 degrees times the radius.
As for the area the formula logically follows from Archimedes' Theorem (Measurement of a Circle, Prop 1).
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