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mg.metric geometry – Kakeya crossed-needles problem
the Kakeya needle problem asks for the minimum area planar region in which one can completely turn around a line segment through a series of translations and rotations. There is no minimum: There are Kakeya needle sets of arbitrarily small area.
I ask the same question but for a rigid plus-sign, two equal-length segments at $90^\circ$ sharing their midpoints, forming a $+$ shape. Because it seems difficult to achieve $360^\circ$ rotation using the type of spikey sets so effective for a single needle, I’m wondering if the answer here might be just a disk?
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