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.

    • dual_sport_dork 🐧🗡️
      3•1 year ago

      For those still in the dark, I’m referencing the bible in 1 Kings 7, 23-26:

      And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about. And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast. It stood upon twelve oxen, three looking toward the north, and three looking toward the west, and three looking toward the south, and three looking toward the east: and the sea was set above upon them, and all their hinder parts were inward. And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

      Those measurements would only work if either the cauldron were not actually circular, or if Pi were equal to 3.