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> Note that the Python version of pi requires an unbounded amount of memory

Really? I measure it as exactly 200 bytes (not counting the 4-space indentation that HackerNews requires, and not including a trailing newline)

> and, more importantly, an infinite amount of time to produce pi to infinite precision

I can see it right now, with infinite precision. If it's taking an infinite amount of time to show up I'd contact your ISP ;)



Ah, I see where you are going with this. However, I can offer a version which, without loss of generality, gives another 200-to-1 compression (not counting UTF-8 multibytes): π.

There it is, in all it's infinite splendor.




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