Gerson's Pi Program

[Gerson W. Barbosa]

(12-28-2020 11:20 AM)EdS2 Wrote:  I'd be interested to know how it works!

Hello, Ed!

Thank you very much for your interest! That’s an MSX BASIC listing. The MSX computer was very popular in Brazil and England in the mid 80’s (but not in the USA). That was my second computer. I liked its 14 significant digits, much better than my first computer, an Apple II clone.

The program is based on this formula:

\(\pi \approx \left ( \frac{4}{3} \times \frac{16}{15}\times \frac{36}{35}\times\frac{64}{63} \times \cdots \times \frac{ 4n ^{2}}{ 4n ^{2}-1}\right ) \left ( 2+\frac{4}{8n+3+\frac{3}{8n+4+\frac{15}{8n+4+ \frac{35}{8n+4 + \frac{63}{\dots\frac{\ddots }{8n+4+\frac{4n^{2}-1}{8n+4}}} }}} } \right )\)


That’s the third Wallis-Wasicki formula, as I called it, rather jokingly. Notice the reuse of the denominators in the Wallis product as the numerators in the continued fraction.

Here’s the thread in which I presented it, in case you missed it:

https://www.hpmuseum.org/forum/post-1394...#pid139434

Best regards,

Gerson.