3 ms·

If space can be curved, non-flat, then can't pi take on a wide variety of values, like near the high curvature of space near a black hole? As I suspected... >

If space can be curved, non-flat, then can't pi take on a wide variety of values, like near the high curvature of space near a black hole? As I suspected... > "Now, some fun facts: for a circle of radius 1000 miles, the value of "π" would be around 3.10867! For a 50 mile radius, "π" would be 3.14151. And even the engineers who built the Large Hadron Collider should have worried about the value of "π", since for a circular structure 2.7 miles in radius (which is the case for the LHC) "π" would be 3.141592415! So, we strongly encourage all high energy physicists and their sympathizers to celebrate Pi Day two minutes earlier than the rest of the world to honor our non-Euclidean geometry! As for the community of general relativity... we encourage them to redo all the calculations in a non-minkowskian metric for a non-massless Earth to know exactly when they should celebrate Pi Day. Also, advocates of the Indiana Pi Bill who root for legally making π equal to 3.2 should probably reconsider and change it to a value smaller than 3.1415926, since no circle on Earth would give them their desired result! Though if the surface of our planet was a saddle, that would be a completely different matter..." https://physics.illinois.edu/news/34508 https://physics.illinois.edu/news/34508

anderskaseorg 4y ago
π is defined as the ratio between a circle’s circumference and diameter in ideal flat Euclidean space. You can measure circles in other spaces and get different numbers, but those numbers are not π. (That’s why your linked article writes π′ or “π” when referring to those numbers.)
- xigoi 4y ago
  Or even better, it's defined as the smallest positive root of the sine function. Much simpler definition.
  - doliveira 4y ago
    But then how do you define the sine function?
    - xigoi 4y ago
      Either in terms of the exponential function, or by its Taylor series.
      - doliveira 4y ago
        Oh yes, much simpler. I guess you can get to "i" via algebraic equations, but linking it to a rotation unit outside a flat space seems tricky.
        xigoi 4y ago
        It's basic calculus. I'm really curious how you define the perimeter of a circle without basic calculus.
        doliveira 4y ago
        Of course you can define it, but it's hard to justify the specific definition without a flat geometry. And you don't need proper calculus for the circumference, just the idea of limits.

anderskaseorg 4y ago

π is defined as the ratio between a circle’s circumference and diameter in ideal flat Euclidean space. You can measure circles in other spaces and get different numbers, but those numbers are not π. (That’s why your linked article writes π′ or “π” when referring to those numbers.)

xigoi 4y ago
Or even better, it's defined as the smallest positive root of the sine function. Much simpler definition.
- doliveira 4y ago
  But then how do you define the sine function?
  - xigoi 4y ago
    Either in terms of the exponential function, or by its Taylor series.
    - doliveira 4y ago
      Oh yes, much simpler. I guess you can get to "i" via algebraic equations, but linking it to a rotation unit outside a flat space seems tricky.
      - xigoi 4y ago
        It's basic calculus. I'm really curious how you define the perimeter of a circle without basic calculus.
        doliveira 4y ago
        Of course you can define it, but it's hard to justify the specific definition without a flat geometry. And you don't need proper calculus for the circumference, just the idea of limits.