Question

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Answer 1

These are 45-45-90 triangles, whose hypotenuses are $\sqrt{2}$ times their legs. Given a side of length 1, for example, the diagonal length is $\sqrt{2}\approx 1.4142.$ The first few ordered pairs $(x,y)$ in the table would be $(1,1.41),(2,2.83),(3,4.24),(4,5.66),...$