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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.
A vector X ∈ R k is multivariate-normally distributed if any linear combination of its components Σ k j=1 a j X j has a (univariate) normal distribution. The variance of X is a k×k symmetric positive-definite matrix V. The multivariate normal distribution is a special case of the elliptical distributions.
The digital divide in the United States refers to inequalities between individuals, households, and other groups of different demographic and socioeconomic levels in access to information and communication technologies ("ICTs") and in the knowledge and skills needed to effectively use the information gained from connecting. [1] [2] [3] [4]
Every prime number p divides a Fibonacci number that can be determined by the value of p modulo 5. If p is congruent to 1 or 4 modulo 5, then p divides F p−1, and if p is congruent to 2 or 3 modulo 5, then, p divides F p+1. The remaining case is that p = 5, and in this case p divides F p.
Tangent line at (x 0, f(x 0)). The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point. Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a ...
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
Nuclear power's contribution to global energy production was about 4% in 2023. This is a little more than wind power, which provided 3.5% of global energy in 2023. [167] Nuclear power's share of global electricity production has fallen from 16.5% in 1997, in large part because the economics of nuclear power have become more difficult. [168]