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 = [画像:a((sint)/t-2cost-tsint)]
(1)
y = [画像: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
CatacausticExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
2dcurves.com. "Atzema Spiral." https://www.2dcurves.com/spiral/spiralat.html.Referenced on Wolfram|Alpha
Atzema SpiralCite this as:
Weisstein, Eric W. "Atzema Spiral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AtzemaSpiral.html