Answer to the home page question: (5π/3)(3√2 − 4)
See Weisstein, Eric W. “Sphere-Sphere Intersection.” From MathWorld—A Wolfram Web Resource. Link.
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Interesting complex valued function
The function $f(z) = \sum_{n=1}^{\infty} \left(\frac{z}{n}\right)^n$ is entire (holomorphic everywhere in the Complex plane). Its behaviour on and near the imaginary axis produces striking spiral patterns.
Project Euler
