# ELIF: Why is Pi the basis of so many mathematical formulas?

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For example pi(r)^2 For the area of a circle and 2(pi)r for the circumference of a circle.

I remember these formulas, but never conceptually grasped why we use a seemingly random number (22/7) and use it in various different formulas for various calculations.

In: Mathematics

Pi is not an invented number but a discovered number. Mathematicians discovered that if you compare the circumference to the diameter of a circle, you get the same ratio. That means that if you measure the outside of a circle and divide it by the distance across the circle, you always get a number incredibly close to 3.14159 (accuracy is dependent on your measurement tool and how “perfect” your circle is).

If you want to know where the area formula comes in, go to the link below and click “Start Show.”

https://www.geogebra.org/m/WFbyhq9d

The number is simply a ratio of a circle’s circumference to its radius, you’re just taking one number divided by another. If you drew a perfect circle and measured these two, you’d get pretty close to Pi. Mathematicians don’t draw circles, but use formulas. Here’s an example:

π = (4/1) – (4/3) + (4/5) – (4/7) + (4/9) – (4/11) + (4/13) – (4/15) …

The more terms you add (following this sequence), the closer you get to Pi.