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Apr 27, 2026 - 04:22

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Relationship between a Pythagorean triple and a Pythagorean quadruple

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	===Relationship between a Pythagorean triple and a Pythagorean quadruple===		===Relationship between a Pythagorean triple and a Pythagorean quadruple===
	Every primitive Pythagorean triple will generate a primitive Pythagorean quadruple. Let (o, e, h) be a Pythagorean triple, where o is the odd leg, e is the even leg, h is the hypotenuse and s = (h+o+e)/2 the semiperimeter of the right triangle formed from the Pythagorean triple. Then		Every primitive Pythagorean triple will generate a primitive Pythagorean quadruple. Let (o, e, h) be a Pythagorean triple, where o is the odd leg, e is the even leg, h is the hypotenuse and s = (h+o+e)/2 is the semiperimeter of the right triangle formed from the Pythagorean triple. Then it is always possible to generate a primitive Pythagorean quadruple as (e/2, s-o, s, h+e/2) (ref to OEIS).
	it is always possible to generate a primitive Pythagorean quadruple as (e/2, s-o, s, h+e/2) (ref to OEIS).

	This is a consequence of the identity		This is a consequence of the identity