I should clarify: The square however does not approach *a* square of fixed size. It is actually unbounded. Rather it "looks" more like a square as N→∞.
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Cosh²(x) + Cosh²(y) = π + 3/4π is approximately the unit circle
Cosh²(x) + Cosh²(y) = N approaches a square as N→∞pic.twitter.com/BowV3xHmjm
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Look at this. x^n + y^n = 1 approaches a square as n tends to infinity!pic.twitter.com/btjpalkyLE
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Sort of like Clifford the Big Red Dog has a "dog shape," though he's the size of a house.
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