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Nielsen's Spiral

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NielsensSpiral

Nielsen's spiral, also called the sici spiral (von Seggern 1993) is the spiral with parametric equations

x(t)=aci(t)
(1)
y(t)=asi(t),
(2)

where ci(t) is the cosine integral and si(t) is the sine integral.

The curvature is given by

kappa(t)=t/a,
(3)

and the arc length measured from t=1 by

s(t)=alnt.
(4)

See also

Cornu Spiral, Cosine Integral, Sine Integral, Spiral

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References

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 146-147, 1997.von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 204 and 270, 1993.

Cite this as:

Weisstein, Eric W. "Nielsen's Spiral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NielsensSpiral.html

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