Sentence examples for ratios of integers from inspiring English sources

At the same time, he added minute gradations, or microtones, until he had a forty-three-tone scale, each interval controlled by ratios of integers.

That work also contains accurate approximations (expressed as ratios of integers) to the square roots of 3 and several large numbers.

He also rejected decimal fractions as inexact (whereas ratios of integers as exact and scientific), and extracted roots of negative numbers thus: − a = a −, a − 2 = − a.

There are two solutions, √2 and -√2, called irrational numbers because they cannot be written as a ratio of integers.

Like the constant, is irrational: it is not a ratio of integers; and it is transcendental: it is not a root of any non-zero polynomial with rational coefficients.

Lightman, a theoretical physicist as well as a novelist, has an atypically data-driven approach to fiction; we learn early on that the invention of music involved "a scale with a fixed ratio of frequencies, generally 2 1/12, since exponential powers of that number came closest to ratios of small integers like 3 2 and 4 3".

Lightman, who is a theoretical physicist as well as a novelist, has an atypically data-driven approach to fiction; we learn early on that the invention of music involves "a scale with a fixed ratio of frequencies, generally 2 1/12, since exponential powers of that number came closest to ratios of small integers like 3 2 and 4 3".

Another difference is that it supports division: whereas the ratio of two integers is usually not an integer, the ratio of two rationals is always a rational.

If, for example, Jupiter and the Sun are the two massive bodies, these stable configurations occur when the mean motions of Jupiter and the small particle here an asteroid are near a ratio of small integers.

Even the Pythagoreans fell into this trap; the depths to which they eventually sank may be judged from the story that they discovered and then tried to conceal the fact that the square root of 2 is an irrational number (i.e., cannot be expressed as a ratio of two integers).

This paper investigates the problem of output-feedback control for a class of stochastic high-order nonlinear systems with a ratio of odd integers power.