Defined for two real numbers as the square root of the sum of their squares
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.[1]
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;[2] it is related to the quadratic mean or "root mean square".
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In mathematics, Pythagoreanaddition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its...
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans...
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known...
Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient...
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...
Pythagorean expectation is a sports analytics formula devised by Bill James to estimate the percentage of games a baseball team "should" have won based...
ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia...
moderation Pythagorean letter – the Greek letter upsilon, used as a symbol by the PythagoreansPythagorean diet – vegetarianism Pythagorean symbol – the...
(that is, RMS(signal) = stdev(signal) if the mean signal is 0). Pythagoreanaddition Average rectified value (ARV) Central moment Geometric mean L2 norm...
in a Pythagorean tuning. The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a Pythagorean comma...
(z)^{2}+\operatorname {Im} (z)^{2}}}={\sqrt {x^{2}+y^{2}}},} the Pythagoreanaddition of x {\displaystyle x} and y {\displaystyle y} , where Re ( z )...
squares. The square root of the sum of two squares, also known as Pythagoreanaddition, is a useful function, because it finds the hypotenuse of a right...
mathematical concepts. He has written several compositions using a non-Pythagorean scale based on logarithms. He has also incorporated prime numbers and...
were detuned by the Pythagorean comma, sounded. With the advent of polyphony in the second half of the 15th century, in addition to the octave and fifth...
Ancient Greek: Φιλόλαος, Philólaos; c. 470 – c. 385 BC) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy...
does not tell us everything there is to know about a particular scale. Pythagorean tuning, or 3 limit tuning, allows ratios including the numbers 2 and...
for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines...
Another major sixth is the Pythagorean major sixth with a ratio of 27:16, approximately 906 cents, called "Pythagorean" because it can be constructed...
This 9:8 interval was named epogdoon (meaning 'one eighth in addition') by the Pythagoreans. Notice that in these tuning systems, a third kind of whole...
is often corrected to 4:3 on the natural horn in just intonation or Pythagorean tunings, but the pure eleventh harmonic was used in pieces including...
multiple definitions of a minor sixth can exist: In 3-limit tuning, i.e. Pythagorean tuning, the minor sixth is the ratio 128:81, or 792.18 cents, i.e. 7...
including an approximation of the square root of 2 and the statement of the Pythagorean theorem. Baudhayana's Śrauta sūtras related to performing Vedic sacrifices...
with only twelve notes to an octave (such as the piano) is tuned using Pythagorean tuning, one of the twelve fifths (the wolf fifth) sounds severely discordant...
thirds closer to pure. Meantone temperaments are constructed similarly to Pythagorean tuning, as a stack of equal fifths, but they are temperaments in that...
and between each corner (segment), there are Pythagorean Devices (ピタゴラ装置, Pitagora Sōchi). "Pythagorean device" is the equivalent Japanese colloquialism...
for measuring length or drawing straight lines. Nor is it designed for addition or subtraction, which is usually performed using other methods, like using...
statements of the Pythagorean theorem, both in the case of an isosceles right triangle and in the general case, as well as lists of Pythagorean triples. In...
four right angles. A square has four right angles, in addition to equal-length sides. The Pythagorean theorem states how to determine when a triangle is...
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