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There are many equivalent definitions and many of them do not refer to geometry at all. If you don't want to go through cos you can always define pi as sqrt(6 *
by IsTom 2y ago
There are many equivalent definitions and many of them do not refer to geometry at all. If you don't want to go through cos you can always define pi as sqrt(6 * sum from 1 to inf 1/n^2).
- TeMPOraL 2y agoYou can also define it as `3.14159...` just because. Obviously, a π definition entirely divorced from geometry becomes irrelevant to it - instead, in geometry, you'd still use π = circumference/diameter, or π = whatever(cos), and those values would happen to be the same as a non-geometric π, but only if the geometric π is the one from Euclidean geometry.
- Tainnor 2y ago> You can also define it as `3.14159...` just because. That's not a rigorous definition, though, because it doesn't tell you what those "..." expand to.