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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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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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