Start with a unit circle, then iteratively circumscribe a regular n-gon (n = 3, 4, 5, 6, ...) and another circle. The sequence of radii converges to the polygon circumscribing constant = 8.7000366... #math #geometrypic.twitter.com/ETS6zFylvF
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there's also a conformal automorphism which lets you zoom in while keeping the limit circle unchanged.