polymathematic
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Saturday 05 March 2022 19:53:57 GMT
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Write Words - Make Magic :
Does this integration not work for other types of shapes with different constants?
2022-03-05 20:05:46
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db_md :
It's more about the fact that r is the fundamental part of a circle, not d. The defn is all points r away from the center.
2022-03-05 20:06:27
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WaterSleeps333 :
I also will take up arms for defending things that are interesting but not useful 😂
2022-03-05 20:57:37
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The Math Tutor :
I am on board with tau, but I'd miss the niceness of the sphere surface area being clearly 4 times the average area of its shadow.
2022-03-05 22:21:14
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MartinK :
All I can say is, I prefer pie to tau, because if I we write tau by hand, the symbol is not as clearly distinguishable as that of pie!
2022-03-05 20:27:22
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user5786482156497 :
The analogy I’ve always seen is to the area of a triangle which Archimedes used to get to the area of a circle iirc the argument
2022-03-05 20:43:25
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Write Words - Make Magic :
I like it more because of its similarity to KE=1/2 * m * v^2
2022-03-05 20:07:23
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Y :
for coding computation the division is incredibly slow with Tau when compared to how fast multiplication especially by 2 is
2022-03-05 23:02:31
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turgutmakbak :
BTW, the volume of a sphere is the integral of its surface area, too. But as you said, the fudge factors we use are a matter of convenience.
2022-03-05 23:34:08
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hyfro_cyrup :
You’re telling me you never even did that as like an exercise in Cal 2
2022-03-06 00:45:49
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Lukas Robin :
i’ve had to integrate circumference to radius for my A level maths last year, it was a related estes problem😐
2022-03-06 00:53:25
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Joe R. :
I think pi^2/6 looks better than tau^2/24. Also yo get the who full circle isn’t technically a function of x thing
2022-03-06 01:19:12
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P.D. :
But before you said it was worse (“quite a bit uglier”). Just saying, it’s not worse, but instead just as good and with some interesting symmetries.
2022-03-06 03:14:18
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Natasha Taylor :
I think defining the area A = ∫2πrdr requires all the complexity of defining it as ∬r ⋅ dθ dr (i.e. having to do calculus) but lacks the flexibility
2022-03-06 07:54:24
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