May 18, 2025
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radians
Radians
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Mr. Taken got us these 3 little mini-pies for Pi Day and we split them so I had ³⁄₂ pies, and my brain was like, ³⁄₂π? I should have heated them up at 270°.
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.
Radians Are Cursed [Explained]
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Why is a circle 360 degrees? The Babylonians, who had a base-60 number system (ours is base 10), created the unit of measurement.
The first person to teach me about radians told me that the fact that a circle had 360⁰ was arbitrary. 360 was a number they just plucked out, incidentally, from the idea that a year had 360 days. Also, of course, an arbitrary fact that we changed to another arbitrary number of 365/366 in leap years with Julius Caesar. Radians are a more natural measure, better for pure mathematics because they're ratios that flow naturally from our already occurring concept of a circle.
If the year is arbitrary, and radians are less so, what if I could measure how old I am in terms of circles? Like a tree has rings in its trunk for how old it is, what if I decided that our time keeping epistemology wasn't as good as describing myself in terms of pi, neverending and irrational?