I think I'm pretty much doing pi approximations in every language now, so here it is in QBasic! However, note that I will not do this in normal BASIC since QBasic just doesn't have the graphics included and doesn't require the number to string conversions.
Here are the other approximations:
Fortran - https://repl.it/talk/share/p-in-Fortran/34890
APL - https://repl.it/talk/share/p-in-APL/34888
Forth - https://repl.it/talk/share/p-in-Forth/34652
LOLCODE - https://repl.it/talk/share/p-in-LOLCODE/34421
Python and Node.js (Node is linked in post) - https://repl.it/talk/share/2-Approximations-of-p-In-Only-Four-Lines-of-Code/32773
C - https://repl.it/talk/share/p-Approximations-in-C/33461
Credit to @TheForArkLD , @Warhawk947 , and @LizFoster for inspiring these approximations. Most of these use the Nilakantha Series, although I also use the arctangent method (multiplying the radian arctangent of 1 by 4 to get pi and getting the arctangent with an infinite series) in three of them (Python, Node, and C).