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Re:Why is e^(pi i) = -1? by mhartl on Monday November 02, 2009 @07:58PM (#918318)
As 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.

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