Why did the first person even ask what it was?
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People building things would have just noticed that the ratio was always the same.
You need to build something circular. To ensure its accuracy (especially if you need to build more than one), you make a jig or pattern. To get started, it’s very easy to sweep out a circle with a nail, a string, and piece of chalk. You need to figure out how much material you need, so you take some measurements of your circle and find out how wide it is and at least a “close enough” estimate of the circumference.
Once you’ve done this on a few different sized circles, you’re going to notice that the circumference is always about three times the diameter. And it’s going to be worth it for you to notice this because now all you have to do is measure the diameter and you know everything about the circle without fiddling with whatever more tedious method you were using to measure the circumference.
Now, you’re a tradesman so you figure it’s 3 or a little more and that’s all you need to know. Then someone like Archimedes rolls around. It’s known there’s this ratio, and no one knows exactly what it is, but everyone is pretty sure it’s always exactly the same. So Archimedes (or someone like him) proves that it is always the same and develops a method for calculating it more accurately. He comes up with 22/7 and that’s close enough for any practical purpose that doesn’t leave the Earth’s atmosphere even today.
Pi is important because it shows up everywhere. This is because trigonometry is based on the unit circle. And if you build something from a circle, pi is simply going to pop out of it at some point. Plus, anything that vibrates or oscillates–anything with a frequency or a wave–can be expressed with sines and cosines. Pi is just baked in to the way we built higher mathematics.
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