The remarkable classical pattern of the Theodorus spiral, or square root spiral, can intuitively be supplemented by a closely related spiral asymptotic to it. A ``nice'' analytic interpolating curve of the Theodorus spiral was constructed by P.J. Davis (1993) as an infinite product satisfying the same functional equation as the discrete points. We consider the analytic continuation of the Davis solution and show that it contains the supplementing spiral as a discrete subset. We also discuss efficient evaluation algorithms as well as asymptotic expansions of the analytic functions involved.

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