This is all about perfectness of a circle.
That the circumference and diameter (and radius) ratios are common to all circles is a discovery if you want to call it that, but this is about Pi itself, which is an exact number, and depends a perfect circle. One can easily calculate an estimate of the circle ratio; 3 is used a lot, but if you want more accuracy, 3.1, or 3.14, etc. All of these are observable and measurable in real world circles, but none of them are Pi.
Pi is what happens when you take our observation / discovery and apply it to an invented perfection: the perfect circle. If we invent the perfect circle, what is the value of the circle ratio? The answer is Pi. This is an invented answer; you can't find an instance of Pi in any real circle.
That the circumference and diameter (and radius) ratios are common to all circles is a discovery if you want to call it that, but this is about Pi itself, which is an exact number, and depends a perfect circle. One can easily calculate an estimate of the circle ratio; 3 is used a lot, but if you want more accuracy, 3.1, or 3.14, etc. All of these are observable and measurable in real world circles, but none of them are Pi.
Pi is what happens when you take our observation / discovery and apply it to an invented perfection: the perfect circle. If we invent the perfect circle, what is the value of the circle ratio? The answer is Pi. This is an invented answer; you can't find an instance of Pi in any real circle.
