So I know that pi is the ratio of a circle’s circumference to its diameter (and the ratio of r³x4/3 to the volume of a sphere).

Apparently even the circumference of the universe needs less than 40 decimal places to be more accurate than we would ever need to worry about.

So my question is, how do we determine the decimal points beyond this? If pi is a ratio and even the largest conceived circle only gets you to ±36 places, how do we determine what the subsequent numbers are?

  • Björn Tantau@swg-empire.de
    4·
    24 hours ago

    Meh, spacetime curvature has so little effect that it actually does come down to measurement accuracy. And if you go to the scale of the whole universe it is flat as far as we currently know.

    Now I wonder how LISA will handle curvature changes due to sun, earth and moon moving around, or if they won’t make enough of a difference.

    • qt0x40490FDB@lemmy.mlEnglish
      2·
      23 hours ago

      I mean, geodetic interferometers already exist and can measure very small deviations. Give them arms the length of the observable universe and they will increase in accuracy, not decrease in accuracy.

    • qt0x40490FDB@lemmy.mlEnglish
      2·
      23 hours ago

      If you constructed a circle with the radius of the universe, then measured its circumference and radius measurement accuracy would easily be able to tell the difference between a real circle and a mathematical circle. That is because neither the perimeter of circle will nor the diameter of the circle will be through in empty space. They will be near enough to matter to measure detectable deflections.