Why does pi exist?

it doesn't exist. It's a concept of an observable ratio. There's no rational explanation for why it's 3.14, it just is. That's like asking why water is wet.

It's a mathematical ratio, and they named it π

π = c/d

c = π d

d = c/π

c = circumference of a circle

d = diameter of a circle

Because it's a ratio. No matter what size the circle is the ratio remains the same.

Think of taking a photo of a circle. It doesn't matter if you're very close and it looks big, or a long way away and it looks small, it's the same circle, and the proportions are always the same.

It's similar to the area of a triangle, always half the height times the base!

What circle? I see straight lines drawn equal angles to many other points finalizing in what appears to be a circle from a distance.

Frankly my take is that it is the simplest of the irrational points that suggest that existence is not "off the rack" and that the sneaky hand of absurdity is behind everything.

I have to admit that I just accept that approximations for π are

π = 22/7 or 3 • 14.

There is a danger of wasting time otherwise.

Pi is just a way of writing the ratio of the circumference of a circle to the diameter of a circle.

It's just a property of a circle that if you divide the circumference of a circle by its own diameter the ratio never changes. That ratio can't be expressed as a decimal number so we assign the Greek letter "p" to it. The Greek letter p (p for perimeter I guess) is written π.

if the diameter of a circle is 1 then the circumference will be 3.14...

the circumeference is 3.14... the amount of the diameter