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In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More particularly, the ratio takes the form: + = + where n is a positive integer. Thus: A superparticular number is when a great number contains a lesser number, to which it is compared, and at the ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The plastic number is also sometimes called the silver number, a name given to it by Midhat J. Gazalé [26] and subsequently used by Martin Gardner, [27] but that name is more commonly used for the silver ratio 1 + √ 2, one of the ratios from the family of metallic means first described by Vera W. de Spinadel.
For a positive integer n, p(n) is the number of distinct ways of representing n as a sum of positive integers. For the purposes of this definition, the order of the terms in the sum is irrelevant: two sums with the same terms in a different order are not considered to be distinct.
The real-number Euclidean algorithm differs from its integer counterpart in two respects. First, the remainders r k are real numbers, although the quotients q k are integers as before. Second, the algorithm is not guaranteed to end in a finite number N of steps. If it does, the fraction a/b is a rational number, i.e., the ratio of two integers
In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio a / b is a rational number; otherwise a and b are called incommensurable. (Recall that a rational number is one that is equivalent to the ratio of two integers.) There is a more general notion of commensurability in group theory.
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio ...
Euclid defines a ratio as between two quantities of the same type, so by this definition the ratios of two lengths or of two areas are defined, but not the ratio of a length and an area. Definition 4 makes this more rigorous. It states that a ratio of two quantities exists, when there is a multiple of each that exceeds the other.