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From: Richard Smith <null@void.com>
Newsgroups: gnu.emacs.help
Subject: thanks - calculate pi fn. in elisp
Date: Tue, 09 Jul 2024 19:48:48 +0100
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Xref: csiph.com gnu.emacs.help:60981

I know this is "help" and for emacs as a program,
but for what it's worth,
sort of as a thanks,
this is what I as a welder and bit of an engineer managed to do
readily on finding there is a formula for calculating the value of
pi...

You will know better ways, but this "scribble" was a nice bit of
learning maths.

Thanks everyone for help along the way

Rich S

--------------------------------

(setq max-lisp-eval-depth (expt 2 20))

(defun h-invnsq (this-n invnsq-sum)
  (if (zerop this-n)
      invnsq-sum
    (h-invnsq (1- this-n) (+ invnsq-sum (/ 1e0 (expt this-n 2))))))

(defun pi-calc (n-to)
  "calculates Pi - arg integer is to how 1/n^2 integer to sum"
  (sqrt (* 6 (h-invnsq n-to 0))))

(= (sqrt 6) (pi-calc 1)) ;; t
(pi-calc 10)    ;; 3.04936163598207
(pi-calc 100)   ;; 3.132076531809106
(pi-calc 1000)  ;; 3.140638056205993
(pi-calc 10000) ;; 3.1414971639472093
             pi ;; 3.141592653589793