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Lots of nice formulas for π have partners for the number ϖ!
Back before Twitter became a Nazi bar, I issued a challenge there: find a whole series of numbers like pi, each with its own bunch of formulas. @duetosymmetry took me up on this and invented the numbers ϖₙ:
https://math.ucr.edu/home/baez//diary/june_2022.html#june_12
π is ϖ₂ and ϖ is ϖ₄. So between them there's another interesting mutant version of pi!
(3/n)
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