Search results
Results from the WOW.Com Content Network
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, 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 ...
The sum of the series is approximately equal to 1.644934. [3] The Basel problem asks for the exact sum of this series (in closed form ), as well as a proof that this sum is correct. Euler found the exact sum to be π 2 / 6 {\displaystyle \pi ^{2}/6} and announced this discovery in 1735.
[2] The purpose of the proof is not primarily to convince its readers that 22 / 7 (or 3 + 1 / 7 ) is indeed bigger than π. Systematic methods of computing the value of π exist. If one knows that π is approximately 3.14159, then it trivially follows that π < 22 / 7 , which is approximately 3.142857.
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two , e.g. 1 / 8 = 1 / 2 3 .
33 is the 21st composite number, and 8th distinct semiprime (third of the form where is a higher prime). [1] It is one of two numbers to have an aliquot sum of 15 = 3 × 5 — the other being the square of 4 — and part of the aliquot sequence of 9 = 3 2 in the aliquot tree (33, 15, 9, 4, 3, 2, 1).
((x),(y) = {239, 13 2} is a solution to the Pell equation x 2 − 2 y 2 = −1.) Formulae of this kind are known as Machin-like formulae . Machin's particular formula was used well into the computer era for calculating record numbers of digits of π , [ 39 ] but more recently other similar formulae have been used as well.
The rule of three [1] was a historical shorthand version for a particular form of cross-multiplication that could be taught to students by rote. It was considered the height of Colonial maths education [2] and still figures in the French national curriculum for secondary education, [3] and in the primary education curriculum of Spain. [4]
For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 2 9 −1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of ...