Monday, December 29, 2008

Knowing the Digits of Pi

I have a side hobby of memorizing digits of pi. I've memorized about 140 digits by now. However, one day, someone directed me to an article saying that only 39 digits of pi ere really necessary, because past that level of accuracy, one can calculate the circumference of the known universe to within the width of a hydrogen atom.

I generally agreed with this, but until today had no real way of testing it. Thankfully, StumbleUpon came to my aid today, and I found a website with a built-in high-accuracy calculator. IT can handle thousands of digits of precision! Yay!

I started to work. I started by calculating the diameter of the known universe (~93 billion light-years) in terms of the width of a hydrogen atom (~2.4 Angstroms, or 2.4*10^-11 meters). The result = 3665954758333333333333333333333333333.333...

Now the trick is to multiply that number by pi with different level of precision.

First up, pi extended to 4000 digits:
Now, pi extended to just 39 digits:

Success! However, I'm not done. Can I still remain within a hydrogen atom's width even with less precision? The answer is yes, you can cut pi down to just 36 decimal places before you tip the scales:



Awesome uber-calculator here:

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