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.

  • AlataOrange@lemmy.world
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    1 year ago

    The answer to your question is as simple as it is unsatisfying. Additional degrees of precision in construction are only as useful as your means to use them.

    If you using your saw can only cut to an accuracy of 1/8 of an inch, than any precision beyond that point is lost as you are unable to actualize it

    However if you are using a saw and you’re now at the point of your personal skill that you’re measuring to the inside or outside of the mark on a ruler, then it is likely time for you to graduate between more precise form of measurement.

    https://youtu.be/qE7dYhpI_bI?si=HCtTbklCA18ZieCh

    This video covers a lot of the interesting points around measurement and how we can never truly be perfectly accurate with any measurement of any non-discreet metric.

    To give a real world example if you are off by a millimeter diameter when building a car engine cylinder it will likely fail.