Here's an odd one I cooked up wandering the streets.(adsbygoogle = window.adsbygoogle || []).push({});

A square (ABCD) has a circumference = 4x. The distance between two given opposed corners (A,C) or (B,D) can be expressed many ways, but two will suffice: doing it in steps (where the distance between AC is 2x) or directly across (where the distance = sqrt2 (x)).

I thought: What would happen if you reduced the size of the steps?

Would you eventually get to the point where 2x = sqrt2)x)?

In terms of physics, you would, as eventually one would reduce the size of the step to <h (planck distance, IIRC, 10^-44 meter) where it becomes immeasurable - at which point the step size practically equals the diagonal, as neither has any useful meaning at that size.

Given the clumpy nature of the universe, you'd probably get tunnelling long before then, but that's a red herring.

What I'm wondering is: where's the mistake? Is dividing by infinity illegal? If so, why? Zero doesn't equal infinity (obviously) but does dividing by infinity = zero?

I'm not a big time math whiz, but I find these subjects interesting.

best to all,

Mr Studebaker

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# 2x = sqrt2(x)?

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