A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several Perron trees gives a region in which the needle in the Kakeya needle problem can rotate, and can have arbitrarily small area.
Perron Tree
See also
Kakeya Needle ProblemExplore with Wolfram|Alpha
References
Falconer, K. J. The Geometry of Fractal Sets, 1st pbk. ed., with corrections. Cambridge, England: Cambridge University Press, 1990.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 128-129, 1991.Referenced on Wolfram|Alpha
Perron TreeCite this as:
Weisstein, Eric W. "Perron Tree." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerronTree.html