If pi is the ratio of a circle's circumference to it's diameter, why is it irrational?
and yes, pi is defined as a ratio:
[quote]π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter; this is the same value as the ratio of a circle's area to the square of its radius. π is approximately equal to 3.14159 in the usual decimal positional notation. Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants.[/quote]
[quote]
In Euclidean plane geometry, π is defined as the ratio of a circle's circumference C to its diameter d:
[img]http://upload.wikimedia.org/math/b/7/0/b70c5a09890747af19db04c5a73e6542.png[/img]
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.[/quote]
- Wikipedia
Because C and d are not integers.
Because it can't be represented as a simple fraction
Do people really care? I mean, we dealt with this in trig, and in AP Phys, and I just punch the pi symbol into my calculator whenever I'm calculating centripedal force or some trig thing.
