xkcd: Coordinate Precision but pi (π)?
I tried looking for some answer but found mostly
- People reciting pi
- People teaching how to memorize pi
- How to calculate pi using different formula
- How many digits NASA uses
In practice, the majority of people will never require any extra digit past 3.14. Some engineering may go to 3.1416. And unless you are doing space stuff 3.14159 is probably more than sufficient.
But at which point do a situation require extra digit?
From 3 to 3.1 to 3.14 and so on.
The community is called “No Stupid Questions”, maybe you could adjust the tone of your answer accordingly.
Maybe rule one should include, “Google it first”? Not a stupid question, but it is a lazy one.
The link you provided doesn’t even answer the question because it only tells you what NASA uses and then what would happen if you used no decimals at all. So your answer is not only rude, but also lazy and unhelpful.
It is helpful because its the definative answer. There’s no authority that would use a higher number of decimals, and their scope is beyond magnitude for any other application.
There’s no authority that would use a higher number of decimals
Cool, but that still doesn’t answer OP’s question.
Never, the highest needed ever in any situation concerning the entirety of humanity is 15.
You’re the type of person that needs to be told /s for a comment dripping in sarcasm to understand its sarcasm, right?
Or the type of person that posts in movie communities about narrative foreshadowing as being an Easter egg, right?
A+B=C
If 15 digits is the highest number of used by the one agency responsible for all things concerning the highest need of detail than no, there is never an instance of needing to use all the known digits of Pi.
That isn’t what they asked! They asked about when it is tolerable to use fewer digits and at what point the loss of precision becomes a concern again. Your responses have nothing to do with that question.
You can calculate this yourself. For example, if you’re working on an object that’s 1m in diameter and you use 3.14 to compute the circumference, then you can expect errors of up to 1m * (3.142 - 3.14) = 0.002m = 2mm.
This is almost the real answer, only in reverse. Find what the appropriate error bounds of your problem is and use continuity (it probably is continuous) to find what decimal expansion you need. Or you could probably just find a solution expressible in pi and pick the decimal approximation needed. Either way, who cares about pi?
Thank you. After thinking about it overnight, I realized I asked a wrong question. Your answer still helps greatly and get me more than half way to satiate my curiosity.
Tolerance grade and example objects that require different grade/minimum pi accuracy is what I was looking for.
Not a direct answer to the question but one thing not noted in other answers is in computing you often work at a higher precision than you need for your final answer as the errors tend to increase each time you do a mathematical operation.
In the world of reasonably powerful hardware (laptops, desktops, servers, smart phones etc.) we’d typically work with 64 bit floating point numbers which gives pi to 15 digits (I think, not at a real computer now so can’t check). because it’s simple to do so even though we don’t need the full precision.
So, in terms of accuracy required, an old structural book I have includes a “functions of numbers” section which has various things including the square, the square root, the log, and the circumference of a circle with that diameter. It shows pi as 3.142. Outside of alignments, I would expect that to be good enough for most civil engineers.
