Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How Many Decimals of Pi Do We Really Need?

jpl.nasa.gov

Post reply on HN
Print view View original

61–70 of 134 posts

Re: How Many Decimals of Pi Do We Really Need?

#61

Post by singlow »

diskcat wrote: post #54
hanniabu wrote: post #45

Earlier quoted context omitted.

It does depend on the size of the observable universe, which we do know because, well, it's observable.

The post i replied to started off with "If you know the diameter of the observable Universe" but if the result it depends on the size of the observable universe then you ought to say "given the size of the observable universe". Starting with 'if' would imply that the result only requires you 'knowing' the size of the obsv. unv. but does not depend on its actual size.

I think the meaning of "If you know," in this case was more like, "If you take as an input."

Re: How Many Decimals of Pi Do We Really Need?

#62

Post by [deleted] »

andrewflnr wrote: post #28
over wrote: post #20

Earlier quoted context omitted.

Inch / foot / yard / mile is a really small range compared to what metric can handle (anything), so in practice most science is done with metric units.

Wide ranges of values are handled exactly the same way in imperial units as in metric: multipliers. You write "0.00023 inches" or "5.48e4 miles", etc. It's just not as pretty.

[deleted]

Re: How Many Decimals of Pi Do We Really Need?

#63

Post by niccaluim »

brador wrote: post #31
wtbob wrote: post #18

Earlier quoted context omitted.

He's an American, writing for an American audience, and thus he's using the units Americans use. There's absolutely nothing more scientific about one set of units or another (although different sets of units may be more convenient in different situations).

It prevents mistakes when we all use the same units and the SI are agreed by an international committee of scientists and engineers. It's one less thing to go wrong.

This isn't flight control software. It's a blog post. There aren't any "mistakes" to prevent. The website is not going to crash into Mars.

Good writers write for their audience. His audience is accustomed to thinking in miles.

Re: How Many Decimals of Pi Do We Really Need?

#64

Post by desdiv »

>The primary purpose of the DATA statement is to give names to constants; instead of referring to pi as 3.141592653589793 at every appearance, the variable PI can be given that value with a DATA statement and used instead of the longer form of the constant. This also simplifies modifying the program, should the value of pi change.

Xerox Basic FORTRAN and Basic FORTRAN IV Manual[0], attributed to David H. Owens.

[0] https://www.textfiles.com/bitsavers/pdf/sds/sigma/lang/90096...

Re: How Many Decimals of Pi Do We Really Need?

#65

Post by brandmeyer »

Not quite Pi, but something very closely related to Pi is retained to extremely high precision in computers.

libm frequently contains 2/pi to very high precision. For example, Newlib's math library contains 476 decimal digits of 2/pi as part of its routines for calculating sine and cosine of numbers outside the range [-pi/4..pi/4].

See e_rem_pio2.c for more. Many of the open source math libraries are ultimately descended from the same root: the Sunpro fdlibm, archived at netlib: http://www.netlib.org/fdlibm/

Re: How Many Decimals of Pi Do We Really Need?

#68

Post by eggy »

justifier wrote: post #55

i wonder if interest in measuring error of previous calculations is what encouraged this direction of computational rigor respecting accuracy encourages a self awareness with an almost conscious stead ignorant error i am always intrigued when it is discussed how a calculation began and the error of the initial values the first known attempt at measuring the speed of light(o) had an ignorant error of ~26% the first kn…

That should be 0.04% not 0.0004%, no? You need to multiply by 100 for percent?

Re: How Many Decimals of Pi Do We Really Need?

#69

Post by KMag »

sago wrote: post #5

In 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.

> Pi = 3, coincidentally, is the Hebrew Bible's approximation too.

Certainly it's not explicitly spelled out. The example I've heard was the outer diameter and inner circumference of a vessel's circular rim were given. Pi comes out to 3 only if the thickness of the rim of the vessel is zero.

Re: How Many Decimals of Pi Do We Really Need?

#70

Post by zhte415 »

jasonkostempski wrote: post #39
drewolbrich wrote: post #26

If you know the diameter of the observable Universe and you want to calculate its circumference with the accuracy of the diameter of a proton, the number of digits of pi that you need is 43.

Would have been so much better if that answer was 42.

It was 42, but in the time it came to get that answer, it kept expanding. So we need a new computer.
Post reply on HN