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by dTal 4421 days ago
Your circle area formula is incorrect - you square the radius first, then multiply by pi. It's quite easy to see why if you substitute tau/2 for pi - 1/2 tau r^2 is clearly the integral of tau * r, where tau radians is a complete circle. Mixing diameter and radius in the same formula and hiding the resulting factor of two in a constant is a pedagogical disaster.