There are mathematical series that will equate to Pi, or more probably converge.

p/4=1-1/3+1/5-1/7+1/9 .............. etc click for Wiki on Leibniz's method. I will be asking questions later (if I can understand the questions).

to calculate to a trillion decimal places requires calculating each term in the series to 10 trillion DP. Which for 3 or 7 (etc) is going to make for 10 trillion X 10 trillion calcs. (well some terms involving multiples of 5 would reduce that, but not much). And there might be shortcuts with multiples of lower numbers, but that assumes near trillion storage capacity.

I guess they have better algorithms and one discovered in 1995 looks to be easier. My brain is beginning to hurt..............