An Ancient Geometry Problem Falls to New Mathematical Techniques | Quanta Magazine
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.
Hasnain says:
I find it fascinating that the proven theoretical bound for squaring the circle requires something like 10^200 pieces while the experimental results are implying the bound might be … 22.
“That left some room for improvement, which is what Máthé, Noel and Pikhurko have delivered. Their pieces, again numbering about 10^200, are simpler in shape and much easier for mathematicians to visualize.
“The big leap here is that you couldn’t draw Spencer and my pieces in ways you can easily see, but with these pieces you can,” said Marks.
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Already, Pikhurko has ideas to further simplify the pieces, reducing their total number and making them less uneven. And Marks has done computer experiments that suggest — but don’t prove — that the equidecomposition can be accomplished with 22 pieces. He believes the minimum number is likely even lower.”
Posted on 2022-02-09T06:58:35+0000