Comment by _0w8t
4 years ago
On more serious note 22.0/7 or 3.1 in base 7 is a rather good approximation sufficient to quite a few problems and good to calculate things in one’s head.
4 years ago
On more serious note 22.0/7 or 3.1 in base 7 is a rather good approximation sufficient to quite a few problems and good to calculate things in one’s head.
Fun fact, 22/7 is only accurate to one part in 2,500, or 0.04%, netting you one extra digit (i.e 3.14 is less accurate with 3 digits but 3.142 is more).
Most remember 3.14159 which is way better than 22/7, but pi has an even better unusual rational approximation, 355/113 gets you two extra digits, it is accurate to one part in 12 million, or 0.000008% . So you have to go to 3.1415927 to beat it.
JPL answers the question: How Many Decimals of Pi Do We Really Need?
> For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.
https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimal...
That's not saying much as it appears to just be double precision, but yeah, rational approximations only save you one or two digits and after a certain point it’s more nerdy to just memorize pi.