I just saw a post saying NASA had calculated the universe to one hydrogen atom using 40 digits of Pi, I’m aware Pi is a very important number but how does it help us to work out distances etc?
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This is the post [here. ](https://reddit.com/r/todayilearned/comments/13j2c24/til_nasa_finds_only_40_digits_of_pi_needed_to/)
You are misunderstanding that statement. It says that _**if** we know the diameter of the universe, **then** 40 digits of pi suffice to calculate the circumference within a single hydrogen atom_.
There is no implication of measuring actual distances or sizes with pi. It all boils down to the universe being about 40 orders of magnitude (that is: a factor of about 10^^40 ) larger than a hydrogen atom.
That piece of trivia (it takes only a certain amount of digits of pi to calculate the circumference of the universe to within the diameter of a hydrogen atom) is all about how many significant figures are actually important, and why memorizing a huge amount of pi is largely pointless, and less about what pi or the circumference of the universe actually are.
The specific amount is calculated by estimating the diameter of the observed universe (which is figured out based on the age of the oldest sources of light we can see and comparing that to the speed of light), and then taking that estimated number and using it to calculate the circumference (diameter * pi) with only the first 37 digits and comparing that to the same calculation but using the first 38 digits. The difference between the two numbers is a specific value. Both calculations give a number greater than 10^(24)m, but the difference between them is less than 5*10^(-11)m, or the radius of a hydrogen atom.
Which kind of makes sense, because 24 (the magnitude of the size of the observable universe) – -11(the magnitude of the size of a hydrogen atom) is 35, which is pretty close to the amount of decimals it takes to make adding more decimals redundant to real life sizes. The difference can be explained by the fact that we are using estimates, which will often add a magnitude of uncertainty or two.
Pi is the ratio of a circle’s circumference to its diameter. You can think of it like this: if a circle has a diameter of 1 inch, then what’s the circumference? Turns out, it’s about 3.14 inches. and if the diameter was 2 inches, then it would be 6.28 inches. If the diameter was 3 inches, then you’d get 9.44 inches circumference and so on. What this means is you can now figure out the circumference of any circle as long as you know the diameter, which is pretty useful for a variety of fields.
The funny thing is, you’d expect this ratio of circumference to diameter to be a nice neat thing, but it isn’t. Pi as a number is often approximated to 3.14, but this is only an approximation. The “real” pi actually has infinite digits after the decimal point, and mathematicians have proved that this infinite series of digits. The more digits we use, the more accurate our calculations get. For most everyday use, 3, 3.1, 3.14, 3.141, 3.1415 all work well enough depending on the situation. We’re talking about small scales, a few metres, maybe a kilometre. When it comes to space, well, space is pretty big. You’ll need more digits, maybe you go up to 10 or 15. But as it turns out, you can get really accurate really fast with pi. You could calculate the size of the universe with just 3 digits, but you’d probably be off by a huge amount. You keep adding digits until you’re sufficiently happy with how accurate it is, which in this case is probably 40 digits given it’s accurate to an unimaginably small length.
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