3 ms·
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 differen
by 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 agoOr even better, it's defined as the smallest positive root of the sine function. Much simpler definition.
- doliveira 4y agoBut then how do you define the sine function?
- xigoi 4y agoEither in terms of the exponential function, or by its Taylor series.
- doliveira 4y agoOh 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 agoIt's basic calculus. I'm really curious how you define the perimeter of a circle without basic calculus.
- doliveira 4y agoOf 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.