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Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one. [6]For example, if a house is worth $100,000 today and the year after its value goes up to $110,000, the percentage change of its value can be expressed as = = %.
In mathematics, a percentage (from Latin per centum 'by a hundred') is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), [1] although the abbreviations pct., pct, and sometimes pc are also used. [2] A percentage is a dimensionless number (pure number), primarily used for expressing proportions ...
In some contexts it is desirable to round a given number x to a "neat" fraction – that is, the nearest fraction y = m/n whose numerator m and denominator n do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit m .
Explicitly state the number of significant figures (the abbreviation s.f. is sometimes used): For example "20 000 to 2 s.f." or "20 000 (2 sf)". State the expected variability (precision) explicitly with a plus–minus sign, as in 20 000 ± 1%. This also allows specifying a range of precision in-between powers of ten.
Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to r. When finished, divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. For example, if r is 5, then the cells considered are: (−5,5) (−4,5)