GolfScript, 7070 85 bytes
;1;''!.2.):t{](.2*.+.*:a@~@*\a(*@)\@}10 2t.+.+t+:T 32t..*.*t*?(:b?*@;\{.@[\].~/\~%10*@\~%T*@}b*;;]("."@
Try it online!+15 bytes because I can't read.
Or, actually, don't. It takes WAY too long. Try this one instead thatTry this online instead, which calculates 54 digits.
Uses the Wallis Product, and a custom integer division algorithm.