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In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem, for a triangle with sides and , this length can be calculated as where denotes the Pythagorean addition operation. This operation can be used in the conversion of Cartesian coordinates to polar coordinates. It also provides a simple notation and terminology for some formulas when its summands are complicated; for example, the energy-momentum relation in physics becomes

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  • Pythagoreische Addition (de)
  • Somme pythagoricienne (fr)
  • Pythagorean addition (en)
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  • Als pythagoreische Addition wird eine der üblichen Addition ähnliche Rechenoperation bezeichnet, bei der die Summe der Quadrate mehrerer Größen berechnet und daraus die Quadratwurzel gebildet wird. Ausgedrückt als Formel ergibt sich die pythagoreische oder geometrische Summe aus den Größen durch: Ihren Namen trägt die Operation in Anlehnung an den Satz des Pythagoras: , wenn und die Kathetenlängen und die Hypotenusenlänge eines rechtwinkligen Dreiecks darstellen. (de)
  • En mathématiques la somme pythagoricienne de deux nombres a et b est le nombre √a2+b2, que l'on peut voir comme la longueur de l'hypoténuse d'un triangle rectangle de côtés de longueurs a et b par le théorème de Pythagore. L'opération associée, l'addition pythagoricienne, est commutative et associative. La somme pythagoricienne peut être calculée efficacement sur machine par un algorithme donné par Moler et Morisson, qui s'avère être une application de la méthode de Halley. (fr)
  • In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem, for a triangle with sides and , this length can be calculated as where denotes the Pythagorean addition operation. This operation can be used in the conversion of Cartesian coordinates to polar coordinates. It also provides a simple notation and terminology for some formulas when its summands are complicated; for example, the energy-momentum relation in physics becomes (en)
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  • Als pythagoreische Addition wird eine der üblichen Addition ähnliche Rechenoperation bezeichnet, bei der die Summe der Quadrate mehrerer Größen berechnet und daraus die Quadratwurzel gebildet wird. Ausgedrückt als Formel ergibt sich die pythagoreische oder geometrische Summe aus den Größen durch: Ihren Namen trägt die Operation in Anlehnung an den Satz des Pythagoras: , wenn und die Kathetenlängen und die Hypotenusenlänge eines rechtwinkligen Dreiecks darstellen. (de)
  • In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem, for a triangle with sides and , this length can be calculated as where denotes the Pythagorean addition operation. This operation can be used in the conversion of Cartesian coordinates to polar coordinates. It also provides a simple notation and terminology for some formulas when its summands are complicated; for example, the energy-momentum relation in physics becomes It is implemented in many programming libraries as the hypot function, in a way designed to avoid errors arising due to limited-precision calculations performed on computers. In its applications to signal processing and propagation of measurement uncertainty, the same operation is also called addition in quadrature. (en)
  • En mathématiques la somme pythagoricienne de deux nombres a et b est le nombre √a2+b2, que l'on peut voir comme la longueur de l'hypoténuse d'un triangle rectangle de côtés de longueurs a et b par le théorème de Pythagore. L'opération associée, l'addition pythagoricienne, est commutative et associative. La somme pythagoricienne peut être calculée efficacement sur machine par un algorithme donné par Moler et Morisson, qui s'avère être une application de la méthode de Halley. (fr)
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