Without looking any of it up, those of you who know the formula for the area of a circle, do you know what "Tau" is in that context?
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i know tau, and i think it's conceptually clearer in trig, circumference, but after answering thepoll i found myself second guessing both my intuition and my recollection of the formula for the area of a circle (haven't used it for years)
I like to think that this is a very intuitive way of remembering that formula. (Imagine the limit of when we split the circle in infinitely many infinitely thin pizza slices.)pic.twitter.com/hsv2pSVoxW
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i like this perspective... my intuition is also geometric but much more simplistic, and i think goes back to struggling with memorizing it in the 6th grade - splitting the circle into quadrants, 4 squares of size r^2 overshoots the area, pi of those squares is the right amount
Thanks. Twitter will use this to make your timeline better. UndoUndo
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... or like this. pretty much the same idea but much better presentation. :D (just popped in my timeline via
@doppioslash)https://twitter.com/FreyaHolmer/status/1202648662049996801 …
the area of a circle is τr²/2
but why?
here's an animation~
by unrolling a circle, it forms a triangle with base τr and height r. we can then apply the triangle area formula of base×height/2 to get the area of the circle, τr²/2
pic.twitter.com/a4LPh1zW6zShow this thread -
this one is lovely! i always have to remind/convince myself the triangle area formula, b*h/2 always seemed too good to be true except for right triangles, next time i stumble i'll try to remember this =)
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