Theodorus Spiral


The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of Theodorus, is a discrete spiral formed by connecting the ends of radial spokes corresponding to the hypotenuses of a sequence of adjoining right triangles. The initial spoke is of length sqrt(1), the next spoke is of length sqrt(2), etc., and each segment of the spiral (corresponding to the outer leg of a triangle) has unit length.

The slope of a continuous analog of the discrete Theodorus spiral due to Davis (1993) at the point (x,y)=(0,0) is sometimes known as Theodorus's constant.

See also

Polygonal Spiral, Spiral, Square Root, Theodorus's Constant

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Davis, P. J. Spirals from Theodorus to Chaos. Wellesley, MA: A K Peters, 1993.Finch, S. "Constant of Theodorus.", W. "The Spiral of Theodorus, Numerical Analysis, and Special Functions.", D. "The Spiral of Theodorus." Amer. Math. Monthly 111, 230-237, 2004.Waldvogel, J. "Analytic Continuation of the Theodorus Spiral." Feb. 2009.

Cite this as:

Weisstein, Eric W. "Theodorus Spiral." From MathWorld--A Wolfram Web Resource.

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