Written: Sept. 9, 2026

In memory of Gila Aharoni (Dec. 8, 1955- Pi Day, 2025)

ל ז כ ר   ג י ל ה   א ה ר ו נ י

Inspired by the polymath Abraham Ibn Ezra who approximated π by 20/9*sqrt(2),
[see Haim Hanani's letter to the editor, that appeared on p. 12 of Joseph Gillis' Gilyonot LeMatematika, Vol. 4, issue 1 (Nov. 1969)],
and RSJ Reddy's masterpiece (in particular this gem), who gave (14-sqrt(2))/4, we point out that both of these approximations are optimal in some sense, and we generate many other ones that are even more optimal, albeit not as nice.

Maple package

• Reddy.txt, a Maple package to find approximations to Pi (and other constants) by radicals in the style of RSJ Reddy)

Sample Input and Output Files for Reddy.txt

• If you want to see Reddy-style approximations to Pi in the form (a-b*sqrt(n))/c, for all n less than, 40, and b and c less than , 100

  The input file gives the output file.

• If you want to see Reddy-style approximations to Pi in terms of sqrt(2) with increasing complexity

  The input file gives the output file.

  (note that the third is his favorite (14-sqrt(2))/4)

• If you want to see succesive approximations of Pi using the PSLQ algorithm

  The input file gives the output file.

• If you want to see Ibn-Ezra style approximations to Pi

  The input file gives the output file.

  (Note that the 4th is his, 20/9*sqrt(2))

Personal Journal of Shalosh B. Ekhad and Zeilberger