#2748: Radians are Cursed
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Transcript
[Title:]
Math facts
[A diagram of a circle is shown with radius labeled as “1”]
The unit circle has a radius of one [In green] ✓ Normal
[The diagram now has another (unlabeled and lighter) radius at a 57.3 degree angle. The arc between the points where the radii intersect the circle is labeled as “1”]
One radian equals the length of a circle’s radius [In green] ✓ Normal
[The diagram now is completely unlabeled except for the arc, which is labeled as “57.3°”]
One radian is 57.3 degrees [In green] ✓ Normal
[The first diagram is shown; however, the radius is labeled as “57.3°”]
The unit circle has a radius of 57.3 degrees [In red] ✗ Cursed
(Sourced from explainxkcd.com)
Title text:Phil Plait once pointed out that you can calculate the total angular area of the sky this way. If the sky is a sphere with radius 57.3 degrees, then its area is 4*pi*r^2=41,253 square degrees. This makes dimensional analysts SO mad, but you can't argue with results.