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# 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 , the next spoke is of length , 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 is sometimes known as Theodorus's constant.

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

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## References

Davis, P. J. Spirals from Theodorus to Chaos. Wellesley, MA: A K Peters, 1993.Finch, S. "Constant of Theodorus." http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.440.3922&rep=rep1&type=pdf.Gautschi, W. "The Spiral of Theodorus, Numerical Analysis, and Special Functions." https://www.cs.purdue.edu/homes/wxg/slidesTheodorus.pdf.Gronau, D. "The Spiral of Theodorus." Amer. Math. Monthly 111, 230-237, 2004.Waldvogel, J. "Analytic Continuation of the Theodorus Spiral." Feb. 2009. http://www.math.ethz.ch/~waldvoge/Papers/theopaper.pdf.

## Cite this as:

Weisstein, Eric W. "Theodorus Spiral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TheodorusSpiral.html