if you want to calculate pi by hand:
- pick a good algorithm. you want something with simple math, but which converges fairly quickly.
- decide in advance how precise you want your solution to be. this will both let you pick how many digits to work out in each calculation and how elaborate the calculation needs to be (e.g. number of terms in a Taylor series)
- use checks - casting out 9s and 11s, for example.
- start small. figure out what kinds of mistakes you make. figure out what tricks will help you.
- if you're not getting anything out of it, stop. remember, 22/7 is accurate enough for most purposes, 355/113 is accurate enough for most others, and if you actually *needed* digits of pi, you could look it up almost anywhere. this is a purely recreational activity.