A set of plane measure 0 that contains a circle of every radius.
Kinney's Set
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References
Falconer, K. J. The Geometry of Fractal Sets. New York: Cambridge University Press, 1985.Fejzić, H. "On Thin Sets of Circles." Amer. Math. Monthly 103, 582-585, 1996.Kinney, J. R. "A Thin Set of Circles." Amer. Math. Monthly 75, 1077-1081, 1968.Referenced on Wolfram|Alpha
Kinney's SetCite this as:
Weisstein, Eric W. "Kinney's Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KinneysSet.html