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$i=\sqrt{-1}$ has no apparent relation with any distance.
Also $\int_0^\infty e^{-x^2}dx=\sqrt{\pi}.$$\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}.$
Also $\int_0^\infty e^{-x^2}dx=\sqrt{\pi}.$
Also $\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}.$
