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Atzema Spiral


AtzemaSpiral

The Atzema spiral, also known as the Pritch-Atzema spiral, is the curve whose catacaustic for a radiant point at the origin is a circle, as illustrated above.

It has parametric equations

x=a((sint)/t-2cost-tsint)
(1)
y=a(-(cost)/t-2sint+tcost)
(2)

where t>=1, which generates a circle of radius 2a.

AtzemaSpiralRays

The sequence of rays generating the circle catacaustic as t is varied from t=1 to t=2pi+1 is shown above.


See also

Catacaustic, Spiral

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References

2dcurves.com. "Atzema Spiral." https://www.2dcurves.com/spiral/spiralat.html.

Cite this as:

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

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