# mg.metric geometry – Kakeya crossed-needles problem Answer

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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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