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Remember that once you set the circumference of a circle, you aren't allowed to choose a radius. So if you set a circumference to be rational, the radius will be irrational. If you set the radius to be rational, the circumference will be irrational.
Being a ratio does not imply a ratio of integers.
I also have a hard time believing you have a BA in math without knowing this. Did you ever study elementary real analysis? Normally that includes at least some study of irrational numbers.
Thanks, I think that I had forgotten to think about the idea of a ratio not necessarily being integers.
As for your comment about having a hrd time believing that I have BA in math without kowing that...well, all I can say to that, beside that I find it relatively offensive, is that this is a question that I started thinking about in the past few months and remember very little Real Analysis. Also, all of my core class were taken in two semesters because I switched my major last minutes, so I think it is fair that I have forgotten some concepts.
I am feeling a little lost about pi. I have been out of college for three years and have a BA in math, so it is silly that I am still trying to figure this out.
I have been told all of my life that pi is the ratio of the circumference to the diamer, and also that pi is irrational.
WELL...how can pi be a ratio and be irrational at the same time? It makes no sense.
The only thing I have been able to figure is that it has something to do with the idea that a circle has no beginning or end and therefore cannot be measured to any exactness.
Any other ideas???
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