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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That’s literally the definition of pi.
If I were to take a circle of diameter d, it’s circumference C will be exactly pi times longer than d.
If I unrolled the circle, it would be just over 3 times longer than the diameter of that circle.
If I rolled the circle along the ground one full rotation, it would travel just over 3 times the diameter of the circle.
C=πd -> π = C/d
That’s all that the ratio of circumference to diameter is saying.
Pick a circle, any circle. Determine the circumference and the diameter (in any chosen unit, millimeters, inches). Divide those numbers. The result is pi.
In reality pi is not directly related to circles, it’s just historically (and technologically) important. Pi is a property of the (complex) exponential function. And if you know anything about math, it’s the most important function.
It’s hard to measure the outside of a circle(circumference). You can’t use a ruler because it’s straight and a circle is not and you can’t use some sort of circular tool because each circle would be unique relative to the tool. But you can measure the diameter quite easily. Its just a straight line.
Through some mathematicians’ work we have learned the ratio of the diameter to the circumference. This ratio is pi or 3.14. What this means is that as the diameter grows the circumference grows 3.14x as fast.
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