That's why they are using 15 decimal places, which in reality, is complete overkill. No instrument I am aware of is capable of measure with such accuracy, top of the line is usually at around 9 decimal places. This is a scale at which relativistic and quantum effects have to be considered.
That pi is 6 orders of magnitude more precise. The nice thing about having 6 and not just 1 or 2 (that would be sufficient) is that you don't have to worry too much about the exponential effect of compound error.
So really 15 decimal places is enough not to worry about pi not adding significant imprecision to your calculation, but not so ridiculous as to waste most of your time processing what is essentially random digits.
That it roughly corresponds to the precision of IEEE754 double precision floating-point numbers is probably no coincidence. This is maths that standard hardware can do really well. More than that requires software emulation (slow) or specialized hardware (expensive).
That pi is 6 orders of magnitude more precise. The nice thing about having 6 and not just 1 or 2 (that would be sufficient) is that you don't have to worry too much about the exponential effect of compound error.
So really 15 decimal places is enough not to worry about pi not adding significant imprecision to your calculation, but not so ridiculous as to waste most of your time processing what is essentially random digits.
That it roughly corresponds to the precision of IEEE754 double precision floating-point numbers is probably no coincidence. This is maths that standard hardware can do really well. More than that requires software emulation (slow) or specialized hardware (expensive).