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John Wallis Pi (Wallis Product)

  1. /*
  2. It was always my affectation even from a child, in all pieces
  3. of Learning or Knowledge, not merely to learn by rote, which 
  4. is soon forgotten, but to know the grounds or reasons of what 
  5. I learn; to inform my Judgement, as well as furnish my Memory; 
  6. and thereby, make a better Impression on both.
  7.  
  8. - John Wallis
  9.  
  10. */
  11.  
  12. i = c = 1
  13. setInterval(_ => {
  14.   for (j = 0; j < 1000; j++, i += .5)
  15.     c *= (~~i * 2) / (~~(i - .5) * 2 + 1)
  16.  
  17.   console.log(c * 2 + '\n' + 3.141592653589793)
  18. }, 16);
π = 2
2 / 1
·
2 / 3
·
4 / 3
·
4 / 5
·
6 / 5
·
6 / 7
·
8 / 7
·
8 / 9
·   · · ·

I was at an old book store a few days ago and randomly picked up History of Mathematics Vol. I by David Eugene Smith 1923 for $7.50. After enjoying flipping around and reading different parts, I pulled up Wikipedia to read more about the author… From there I found some interesting quotes from talking about John Wallis – when I saw the Wallis Product I was inspired to write a quick snippet.

// golfed // javascript // math // pi
snippet.zone ~ 2021-22 /// {s/z}