Is it possible to construct a system of mathematics where pi is a rational number?

Is it possible to construct a system of mathematics where pi is a rational number?

Not if it is defined as the ratio of a traditional circle's diameter to its circumference. If you choose to defined it in any other way then it is no longer pi in the popular sense.

What if the system is 1=Pi?

Yea, create a number set on k(pi/n) where n is all real numbers.

Pi/1

Finite extentions of Q

Q + Q pi

then circles are fucked. Imagine a circle with equal diameter and perimeter. Stop breaking math user, shit's fine the way it is.

[math] \pi = 2\cdot \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots [/math]

>Stop breaking math user, shit's fine the way it is.
>can only into Euclidean geometry

Dumb gorilla poster

sure, if you feel like redefining what a circle is

Base [math]\pi[/math]

[math] \pi = Imaginary{( \space ln(-\mathbb{N}))} [/math]

>irrational numbers

>pi is defined as a ratio
>pi is not rational

fuck maths

Sure. In a geometry defined by the Manhattan norm, the equivalent of pi is 4.

> ratios are rational
kek'd

more that a foundation of geometry is that the radius and circumference cannot both be rational

Pi is a number. Changing mathematics isn't going to change the fact that this number isn't a ratio of integers.

Pi is a concept and not a number.

This.

Q[[π]]