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As a circle expands, its area grows proportional to its circumference. The circumference is proportional to the radius. So you're getting the area by integrati
by johnaspden 17y ago
As a circle expands, its area grows proportional to its circumference. The circumference is proportional to the radius.
So you're getting the area by integrating a linear thing.
- deleted 17y ago[deleted]
- mhartl 17y agoAs a circle expands, its area grows proportional to its circumference. The circumference is proportional to the radius. Exactly. In symbols, this reads dA/dr = C ∝ r. Setting τ = C/r = 6.2831853…, we have dA = C dr = τ r dr => A = ½ τ r². Q.E.D.