How Many Decimals of Pi Do We Really Need?
jpl.nasa.gov
How Many Decimals of Pi Do We Really Need?
1–10 of 134 posts
Re: How Many Decimals of Pi Do We Really Need?
#215 digits is about the precision hand-held calculators provide, right? Many early NASA missions took HP calculators along in missions with trajectory routines in case the computer failed.
Re: How Many Decimals of Pi Do We Really Need?
#3This overlooks the issue that for repeated calculations, such as numerical integration, the trouble comes from accumulated roundoff errors. Even 16 digits of precision can become 0 digits pretty quickly if you're not very careful.
Re: How Many Decimals of Pi Do We Really Need?
#4In this particular case, they’re just using a standard double precision IEEE 754 floating point number. So I assume they do all of their arithmetic (“for JPL's highest accuracy calculations”) using double precision floats.
Re: How Many Decimals of Pi Do We Really Need?
#5In the 'Frontiers in Astrophysics' course on Open Yale, professor Bailyn says that, for the purpose of the course, pi = 3, and pi^2 = 10.
Pi = 3, coincidentally, is the Hebrew Bible's approximation too.
Re: How Many Decimals of Pi Do We Really Need?
#6In the 'Frontiers in Astrophysics' course on Open Yale, professor Bailyn says that, for the purpose of the course, pi = 3, and pi^2 = 10. Pi = 3, coincidentally, is the Hebrew Bible's approximation too.
When I took astronomy, anything within an order of magnitude (10) was considered to be the same number. Calculations are very easy when you're only worrying about the number in the exponent.
Re: How Many Decimals of Pi Do We Really Need?
#7In the 'Frontiers in Astrophysics' course on Open Yale, professor Bailyn says that, for the purpose of the course, pi = 3, and pi^2 = 10. Pi = 3, coincidentally, is the Hebrew Bible's approximation too.
When I took astronomy, anything within an order of magnitude (10) was considered to be the same number. Calculations are very easy when you're only worrying about the number in the exponent.
In astronomy, you only need to get the order of magnitude right to within an order of magnitude.
Re: How Many Decimals of Pi Do We Really Need?
#8Doesnt seem like you need that many digits of Pi when working with green screens and premiere.
Re: How Many Decimals of Pi Do We Really Need?
#915 digits is about the precision hand-held calculators provide, right? Many early NASA missions took HP calculators along in missions with trajectory routines in case the computer failed.
BTW, the computers in the ship were also made by HP.
There is a great story about an incident where a waste recycling problem caused a mission to be aborted. There was urine all over the inside of the capsule. NASA publicly reported that it was a computer failure.
Unfortunately HP had just done an ad campaign about their computers in space. HP sued and NASA settled for an unknown amount.
Re: How Many Decimals of Pi Do We Really Need?
#1015 digits is about the precision hand-held calculators provide, right? Many early NASA missions took HP calculators along in missions with trajectory routines in case the computer failed.
Handheld calculators typically get between 8 and 12 digits of precision. A four-function calculator will top out at 8; a scientific calculator will offer more (plus scientific notation support).
15 digits is about what's offered in double precision floating point calculations.