3 ms·

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.