I remember asking my math teacher this when we first learned irrational number but they said they didn’t know. Not sure if it’s just a stupid question or not.
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Is there any reason why it *should* be a rational number?
Is there any reason why the length across a circle should be an exact fraction or multiple of the length around the outside of a circle?
Similarly, if you draw a square, and the diagonal across the middle, is there any reason why that diagonal should be a multiple of the length of the side of the square?
To respond to another question you’ve asked, irrational numbers do exist in the real world to the extent that any other number (maybe other than 1 and 0) exists. You cannot have exactly 1/2 of something, and without getting into too much philosophy you cannot have 3 of something (either you have one thing, and a different thing, and another thing, or you have one three-thing). Numbers are mathematical constructs that are useful for understanding the world.
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