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A superparticular number is when a great number contains a lesser number, to which it is compared, and at the same time one part of it. For example, when 3 and 2 are compared, they contain 2, plus the 3 has another 1, which is half of two. When 3 and 4 are compared, they each contain a 3, and the 4 has another 1, which is a third part of 3 ...
In mathematics, the plastic ratio is a geometrical proportion close to 53/40. Its true value is the real solution of the equation x 3 = x + 1. The adjective plastic does not refer to the artificial material, but to the formative and sculptural qualities of this ratio, as in plastic arts. Squares with sides in ratio ρ form a closed spiral
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.
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 distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.
where s x 2 and s y 2 are the variances of the x and y variates respectively, m x and m y are the means of the x and y variates respectively and s xy is the covariance of x and y. Although the approximate variance estimator of the ratio given below is biased, if the sample size is large, the bias in this estimator is negligible.
The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
Unlike the ratio, the difference between π(x) and x / log x increases without bound as x increases. On the other hand, Li(x) − π(x) switches sign infinitely many times. Let π(x) be the prime-counting function defined to be the number of primes less than or equal to x, for any real number x.
The area of the selection within the unit square and below the line z = xy, represents the CDF of z. This divides into two parts. The first is for 0 < x < z where the increment of area in the vertical slot is just equal to dx. The second part lies below the xy line, has y-height z/x, and incremental area dx z/x.