Math but painful

Some cooking with math terminology:

The golden ratio and pi are irrational, meaning that they cannot be represented by a ratio.

Yet both the golden ratio and pi ARE represented by a ratio, with pi being the ratio between the circumference and diameter and the golden ratio can be represented like this:

(1 + √5) / 2 ← ratio!

What makes it even more ironic is that phi (the golden ratio), IS LITERALLY CALLED A RATIO!
So where did we go wrong in math to mess up this badly?
Where there’s something I forgot to tell you, irrational numbers are actually just numbers that cannot be represented as a ratio between two integers. So, in reality, there really are no shenanigans here, just a funny way of twisting definitions. Still, I do think it is funny that the golden ratio is called a ratio when it’s irrational.