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Nobody knows how many sets you need to chop up a square and rearrange them to form a circle of equal area!! I'm talking Borel sets - @arula-ratnakar.bsky.social's favorite kind of set. Marks and Unger proved it can be done. Here Marks claims you can do it with ~10²⁰⁰. But how many do you need?
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Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.
www.quantamagazine.org
An Ancient Geometry Problem Falls to New Mathematical Techniques | Quanta Magazine
John C. Baez