I'm trying to understand irrational numbers as the result of comparing different referential symmetries, and I'd like to know if there have been any attempt to explain irrationality from any geometrical point of view.
2026-04-03 23:04:07.1775257447
Is there any attempt to explain irrational numbers from a geometrical point of view?
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Considering the pythagorean theorem on isosleces triangles:
Sidelength of a,b = 1 -> $ c = \sqrt2 $
Sidelength of a,b = 2 -> $ c = \sqrt8 $
...
$ c = \sqrt{(2*a^2)} = \sqrt2*a $
However no matter how big you choose a and b to be as long as they are both rational, you never get a result which is not irrational. One would assume though if you construct it on paper, and $\sqrt2$ was a rational number, then you could find a solution which has an integer distance as side c. But this is never the case.
after seeing Rahuls comment (ofc choices like a = $\sqrt2$ break this)