Without using numbers, Calculate Pi

Question

^{Inspired by Nicola Sap's Challenge}

Goal

Your challenge is to simply produce π with 2³²-1 digits. However today's twist, like the title implies, is to produce it without using any numbers or any π constants in your source-code.

Input/Output

Your program will not be provided usable input. It can output in any reasonable format.

Rules

• Standard Loop-Holes forbidden
• You cannot use numbers in your source code nor can you use a pi constant if it exists. If your language also has tau defined as 2pi, that's also banned. Numbers are in the range [0-9]
• You must output as many digits as you can You must output 2^32-1 digits of pi, including the 3. (This has been changed due to the arbitrary nature of the original task)
• Your Program must terminate, or at least theoretically terminate given enough time. Crashing is an acceptable way to terminate.

Scoring

This is code golf so shortest answer wins.

A Million Digits of Pi for your use

Answer 1

Perl 6, 67 bytes

{$!=.FatRat²/$!+$_+$_-?e}for ²…¹;say substr ⁴/$!,^²³²

Try it online!

Takes a very long time to compute. As an example here's an altered version that only prints the first 1000 digits.

Answer 2

Mathematica, 42 39 bytes

N[Log[-(d=I/I)]/I,((c=d+d)^c^c^c)^c-d]&

Output Returns exactly 4294967295 digits as requested.

If more digits were allowed, then by outputting 7.76e17 digits (if even possible lol), 26 bytes would be possible:

N[Log[-E/E]/I,E^(E^E*E)]&

Sorry but Pi = Ln(-1)/i.

Answer 3

GolfScript, 70 85 bytes

;''!..):t{](..+.*:a@~@*\a(*@)\@}t.+.+t+:T t..*.*t*?(:b?*@;\{.@[\].~/\~%T*@}b*;;]("."@

+15 bytes because I can't read.

Try it online!

Or, actually, don't. Try this online instead, which calculates 4 digits.