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At which scale (real world day to day life situation) when each extra digit of pi become necessary? (kbin.social)

submitted 9 months ago* (last edited 9 months ago) by [email protected] to c/[email protected]

45 comments fedilink hide all child comments

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

Update question to be more specific

In case someone see this later, what is the most advanced object you can build or perform its task, with different length of pi?

0, 3 => you can't make a full circle

1, 3.1 => very wobbly circle

2, 3.14 => perfect hole on a beach

3, 3.142 => ??

4, 3.1416 => ??

5, 3.14159 => ??

Old question below

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.

My non-existing rubber duck told me I can just plug these into a graphing calculator. facepalm

y=(2πx−(2·3.14x))

y=abs(2πx−(2·3.142x))

y=abs(2πx−(2·3.1416x))

y=(2πx−(2·3.14159x))

Got adequate answer from @dual_sport_dork and @howrar
Any extra example of big object and its minimum pi approximation still welcome.

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[–] [email protected] 8 points 9 months ago

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.