I understand that it IS pi, but I don’t understand what “ratio of the circumference of any circle to the diameter” means.
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Let’s say instead of math problems you are dealing with something real. Maybe you have a swimming pool that is perfectly round. You want to place a rope along the edge of the swimming pool all the way around. Why are we doing this? I dunno. It’s more interesting than math problems. You don’t know how long it is around because the only thing you have to measure is straight and it reaches across the pool from one end to the other, right over the center of the pool. The pool is 10 feet across. That’s a diameter. Your pool is 10 feet across.
It seems to make sense that since we know how “big” the circle is, we can also know how far around it is. There is a way to calculate it. That number is pi.
So how much rope do we need? Well, we figure we’ll need at least 10 feet since it’s longer around the whole thing than it is across. So we lay out 10 feet of rope along the edge of the pool. It goes just about a third of the way around. If we envision it like a piece of pie (unrelated word, but the ramification are uncanny), the rope the length of the diameter of the pool, takes up about not quite one third of the whole pie, like a pie cut into pieces for three people (about 120 degrees each slice).
But that’s not big enough to go all the way around, how about another piece of 10 foot rope – that goes around almost 2/3 the way around the pool. Almost. We’re getting there. So let’s get another piece of 10 foot rope and add it, this look like it might do the trick. Except it doesn’t. We put out 3 pieces of 10 foot rope around the pool of 10 feet diameter across, and we have a little bit left. It appears to be about a foot left. So now we cut off a foot of another piece of 10 ft rope and add that. So we have 3.1 pieces of 10 foot rope going around the pool. Almost, there’s still a small gap. We measure it and we figure it is 0.04 the size of the 10 foot piece of rope, so we cut that off and add it. But wait, there’s still a little tiny gap left. For practical purposes were probably done and we can round off and call it a day. For the math problem though, we are not.
The problem isn’t really that pi is “irrational” but rather than we are trying to represent pi in our system which is based on 10. Trying to jam pi into pieces of 10 doesn’t work, there’s always a little tiny bit leftover.
But that’s the idea – the way around the circle is a little bit more than 3 times across the circle.
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