منابع مشابه
Beyond Pythagoras
This paper discusses the new harmonic possibilities enabled through the implementation of Sethares’ theory of the dissonance curve in Max/MSP and its use in a live electronic composition by two of the authors.
متن کاملRelieving and Readjusting Pythagoras
Bill James invented the Pythagorean expectation in the late 70’s to predict a baseball team’s winning percentage knowing just their runs scored and allowed. His original formula estimates a winning percentage of RS/(RS+RA), where RS stands for runs scored and RA for runs allowed; later versions found better agreement with data by replacing the exponent 2 with numbers near 1.83. Miller and his c...
متن کاملPythagoras Numbers of Fields
The study of sums of squares in a ring or a field is a classic topic in algebra and number theory. In this context, several questions arise naturally. For example, which elements can be represented as sums of squares, and if an element can be written as a sum of squares, how many squares are actually needed ? For instance, for an integer n to be a sum of squares of integers, we must obviously h...
متن کاملConsistency and Pythagoras
Pythagorean win share has been one of the fundamental contributions to Sabermetrics. Several hundred articles, both academic and non-academic, have explored variations on Bill James’ original formula and its fit to empirical data. This paper considers a variation that is previously unexplored on any systematic level, consistency. After discussing several important contributions to the line of l...
متن کاملThe Modular Tree of Pythagoras
The Pythagorean triples that are relatively prime (called the primitive triples) have the elementary and beautiful characterization as integers x = m2 − n2, y = 2mn, z = m2 + n2 (when y is even) for relatively prime integers m and n of opposite parity. One can think of this as replacing the parameter t for the circle with the fraction m/n and then scaling. Our motivation for understanding the t...
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ژورنال
عنوان ژورنال: Revista Archai
سال: 2019
ISSN: 1984-249X,2179-4960
DOI: 10.14195/1984-249x_27_9