Here's an interesting dilemma:

We know Pi is an irrational number; mathematicians have proven it to be so.

But its definition says that it is a RATIO of the circumference and the diameter of any circle.

Now, when you divide a rational number by another rational number, you get a rational number.

Doesn't this seem like a contradiction?

In the words of a certain visitor to my site:

*In the equation where the circumference is divided by the diameter, when the circumference and diameter are rational values, why is it that the quotient can be an irrational quantity?*

**The solution**

First of all, like a commenter pointed out, Pi being a ratio of two numbers does not mean it is rational. Pi has been established as irrational, and we know

Pi = C/d, where C is the circumference and d is the diameter of some circle.

It follows that either C or d or both have to be irrational!

This is kind of amazing to think about, but it's true: for any circle, either the circumference, or the diameter, or both a…