I think you’ve heard that trivia wrong. NASA uses 15 decimals of pi. The curiosity is that they don’t need to use more decimals even if many more are known.
I can’t think of any good reason to use 10 instead. The consequence would be if the galaxy is 157 trillion miles or 500 trillion miles away. That’s alot of space to disregard for no good reason.
Really depends on the situation. If you have to land an aircraft on the moon, you better get the value of π right.
However when estimating the distance to another galaxy, you’re not gonna fly there so you just want to know the order of magnitude: is it 10^9 or 10^15 miles away?
I’m referring to Fermi estimations. Yes, NASA uses 15 decimal points for pi, but astronomers aren’t always making super precise calculations. As I mentioned in my previous comment, it’s used for estimating orders of magnitude. It’s helpful when precise calculations are complex, because any error along the way could be obscured or glossed over. A decent fermi estimation will help you identify when your precise calculation is wrong. This estimation can often be done quickly with very little actual data, because you’re only looking at orders of magnitude and rough numbers.
Let’s say you’re trying to calculate something complex. Your Fermi estimate takes like two minutes, and says that the answer is probably in the ballpark of ten million. Your precise answer takes an hour, and comes out to be nearly a billion instead. You can look at your fermi estimate for a minute or two to see if you missed a zero or two somewhere. And if you didn’t, then you need to scrutinize your complex calculation because you know you made an error somewhere.
I think you’ve heard that trivia wrong. NASA uses 15 decimals of pi. The curiosity is that they don’t need to use more decimals even if many more are known.
I can’t think of any good reason to use 10 instead. The consequence would be if the galaxy is 157 trillion miles or 500 trillion miles away. That’s alot of space to disregard for no good reason.
Really depends on the situation. If you have to land an aircraft on the moon, you better get the value of π right.
However when estimating the distance to another galaxy, you’re not gonna fly there so you just want to know the order of magnitude: is it 10^9 or 10^15 miles away?
It may be a joke from xkcd, but I am not sure anyone in their right mind would bother using 10 instead of 3 or whatever.
https://xkcd.com/2205/
possibly relevant in the context: https://www.explainxkcd.com/wiki/index.php/2205:_Types_of_Approximation
Holy shit a site that explains xkcd jokes. You just made my whole week.
Let’s not pretend none of us have ever not understood an xkcd comic.
My brother has a PhD in astrophysics and he said similar likes like pi is 10.
I’m referring to Fermi estimations. Yes, NASA uses 15 decimal points for pi, but astronomers aren’t always making super precise calculations. As I mentioned in my previous comment, it’s used for estimating orders of magnitude. It’s helpful when precise calculations are complex, because any error along the way could be obscured or glossed over. A decent fermi estimation will help you identify when your precise calculation is wrong. This estimation can often be done quickly with very little actual data, because you’re only looking at orders of magnitude and rough numbers.
Let’s say you’re trying to calculate something complex. Your Fermi estimate takes like two minutes, and says that the answer is probably in the ballpark of ten million. Your precise answer takes an hour, and comes out to be nearly a billion instead. You can look at your fermi estimate for a minute or two to see if you missed a zero or two somewhere. And if you didn’t, then you need to scrutinize your complex calculation because you know you made an error somewhere.