a surprising fact about numbers

Here's a fact about numbers that is guaranteed to surprise you. It starts with the simple question: Given two numbers, what is the probability that they have no factors in common? Surprisingly it has to do with a number you may or may not have seen before. Finally, I give a cool application to lattices and shadows.

Sum of 1/n^2: https://youtu.be/YMleINbiNlE
One third of integers are even: https://youtu.be/XG3rOsATZZU
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Thank you Juliette Bruce for suggesting this idea!

Видео a surprising fact about numbers канала Dr Peyam