h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Greetings! I think a more natural starting point for irrational numbers is with roots. Some numbers, such as 36, 49, 121, have square roots. This naturally leads to numbers such as 39, 51 and 67 which do not. Pi is pretty easy to get at because it is the ratio of the circumference of a circle to its diameter, but e is more difficult and abstract.

Indeed it is better to start with the square root of 2 as an example to an irrational number (it is the length of a diagonal of a square, and the root of the polynomial: X^2 - 2 = 0). And then go to an example of a Transendential (I have no idea ho to spell this word) number (like Pi and e) that is no roots of a polynomial with rational coefficients.

May I enter into this conversation by remarking on how it's kind of ironic that maths, the most rational of all languages, has proven that there are infinitely more irrational numbers than rational ones.

Or maybe we're just irrational beings who can't see rationality staring us in the face.

either way, i reckon it to be another nice little silly thing.