Pi in Pascal's Triangle (2014)

by senfiaj on 6/6/2025, 12:38:16 PM with 14 comments

  • by JohnKemeny on 6/9/2025, 10:12:04 PM

    π - 2 = 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••

    That's beautiful. I wonder why the -2 is there, though. To fix it, we would need

    π = -x + 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••

    where x = 2, and so it would be

    π = -1/½ + 1/1 + 1/3 - 1/6 - 1/10 + 1/15 + 1/21 - 1/28 •••

    which makes the -1st triangle number ½, I guess.

  • by raldi on 6/10/2025, 5:05:18 AM

    Even after reading this, I don't understand what pi has to do with 4, 20, 56, 120, 220, 364

  • by lixtra on 6/9/2025, 7:24:39 PM

    (2014) [1]

    [1] https://web.archive.org/web/20140901000000*/https://www.cut-...

  • by nimonian on 6/9/2025, 11:59:00 PM

    There's a typo in the final line of math. I think 1/7C2 should be positive rather than negative.

  • by zkmon on 6/9/2025, 9:29:42 PM

    I wonder if the triangle hides any secrets related to prime numbers as well.