Pythagorean addition

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In mathematics, Pythagorean addition is the following binary operation:

$a \oplus b = \sqrt{a^2+b^2}.$

The name recalls the Pythagorean theorem, which states that the length of the hypotenuse of a right triangle is a ⊕ b, where a and b are the lengths of the other sides.

This operation provides a simple notation and terminology when the summands are complicated; for example, the energy-momentum relation in physics becomes

$E = mc^2 \oplus pc.$