Math question: how do we get an irrational number pi from the ratio of circumference and the diameter of a circle?
Math question: how do we get an irrational number pi from the ratio of circumference and the diameter of a circle?
I am wrong in thinking the circumference or the diameter of a circle has to be rational?
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What's interesting is that no matter how big or how small your circle is, pi is a constant ratio of the diameter to the perimeter (or circumference) of your circle. If you were to cut a string to the length of your circle's diameter, it WILL take 3.14 lengths of string to wrap around the circle (or π times). That's where that number comes from.
Because of this ratio, there will never be a situation in which both the diameter and circumference are both rational numbers at the same time. Either your Diameter is a rational number or your circumference. For example:
P=πD
If D=1... Then P=π(1) or P=π
If P=1... Then P=π(1/π) where D=(1/π)
Logical numbers?
*rational
Good catch. Fixed. I apparently suck with words sometimes. Intent good. Execution flawed. :)
huh - I never thought of it that way but of course it makes total sense.
I love this question - simple but thought provoking!
If you were to cut a string to the length of your circle' diameter, it WILL ALWAYS wrap around by 3.14159 (or π times).
Isn't that backwards?
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Nope.
The equation is P=πD. Meaning the Perimeter is equal to 3.14 times the length of your Diameter.
You can visualize it here: https://m.youtube.com/watch?v=1lQfERPjkzk
Right, so you'd need 3.14 strings of length D to cover the circle, D wouldn't wrap around it itself.
It was implied that it would wrap around the circle. I'll update original post to clarify better.
Yeah that's what I gathered, but it's backwards. C = Pi D means you need pi strings, not that it'll cover the circle pi times.
Ahhhh. I see what your saying. It's fixed.
Yeah. Did not mean to intend that it wraps fully around the circle pi times. Good catch.