It does not relate to it
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You can use pythagorean theorem twice to find the diagonal of a cube
pythagorean theorem was named from a greek mathemition called pythagorus (I think that's how you spell it)
The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.
Pythagoras
Pythagorean theorem