# Why do we consider $\pi$ as a irrational number? [closed]

Why do we consider $$\pi$$ as a irrational number? Why is that? We all know that $$\pi$$ is the solution of circumference / diameter of a circle and there could be infinite amount of circles which can have circumference and diameter in the form of positive integers? Then why is that?

## closed as off-topic by Eevee Trainer, José Carlos Santos, Javi, Joel Reyes Noche, YankoApr 24 at 12:57

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• Because someone proved it. – Mauro ALLEGRANZA Jan 24 at 10:31
• We consider $\pi$ as an irrational number because it is an irrational number. – Joel Reyes Noche Jan 24 at 10:34
• Can you recall what an irrational number is? What is your definition of a circle? What do you call consider in mathematics? Can you give an example of a circle having integers for both circumference and diameter? – mathcounterexamples.net Jan 24 at 11:34

A first step in proving this, is to prove that the ratio of the circumference to diameter is the same for all circles. This ratio is called $$\pi$$. It has long been proven that this ratio is irrational, though there is no proof (yet) that is as elementary as the definition of $$\pi$$ itself. See the Wikipedia page for a few examples of proofs.