I remember my H.S. algebra text had one of those boxed enrichment thingies on one page, that described the spiral of Theodorus and called it the "square-root sprial". Philip Davis in his book Spirals from Theodorus to Chaos, (A. K. Peters, Wellesley, MA, 1993) describes a formula for a smooth spiral interpolating the discrete points of the square-root spiral: T(x) = Prod_{k=1...oo} [(1 + i/sqrt(k)/(1 + i/sqrt(x + k))], -1 < x < oo. (This looks fairly close, at least, to what David wrote below.) In the March, 2004 American Mathematical Monthly, Detlef Gronau proves some characterizations of T as the unique interpolating function with certain nice properties: "The spiral of Theodorus", pp. 230-237. --Dan -------------------- David wrote: << I concocted the Spiral of Theodorus myself once. Though I figured it wasn't original, I am chagrined that I was beaten by 2500 years. It seemed clear to me that the vertices lie on some natural smooth curve. In the complex plane, the nth vertex is PROD(k = 1 to n; 1 + i/sqrt(k)) The best I could do with this is 1/sqrt(n!) PROD(k = 1 to n; sqrt(k) + i) which led me to believe the smooth curve might be akin to the gamma function, that is to say, well beyond my abilities.

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele