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.

someone ELI5 please.

In: Mathematics

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.

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

Well pi is not equal to 22/7, that’s just an approximation. Pi is not a rational number, it cannot be written as a ratio of integers (whole numbers).

The reason pi comes up in equations involving circles is because pi is *defined* to be the ratio of the circumference of a circle to its diameter. It may not be obvious, but this ratio is the same for every circle. In other words, if you take any circle, measure the circumference and then measure the diameter, and then divide these two numbers, you will get the number pi every time (assuming that your measurements are perfect and have no error).

So the formula C = 2*pi*r comes right from the definition. And many other quantities involving circles will in some way relate to pi.

Because many mathematical formulas have circles or spheres in them. Even when formula don’t looks like there’s any circle’s involved, if you see Pi appears in some formula – there’s something circular in it. Like, y^(2)+x^(2) = R this defines circle, though it could look like it’s has nothing to do with it, because there’s no sin or cos. And if you analyze this equation, you’ll see Pi. This is obvious example because we know that this equation defines circle, but in math there’s many not so obvious examples (I just don’t remember them…)