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The eleven character YouTube video identifier (64 possible characters used in each position), allows for a theoretical maximum of 64 11 or around 73.8 quintillion (73.8 billion billion) unique ids. YouTube announced that it would remove video responses for being an underused feature on August 27, 2013. [ 96 ]
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 . In Unicode, precomposed fraction characters are in the Number Forms block.
1 ⁄ 7: 0.142... Vulgar Fraction One Seventh 2150 8528 ⅑ 1 ⁄ 9: 0.111... Vulgar Fraction One Ninth 2151 8529 ⅒ 1 ⁄ 10: 0.1 Vulgar Fraction One Tenth 2152 8530 ⅓ 1 ⁄ 3: 0.333... Vulgar Fraction One Third 2153 8531 ⅔ 2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ...
To calculate the convergents of π we may set a 0 = ⌊ π ⌋ = 3, define u 1 = 1 / π − 3 ≈ 7.0625 and a 1 = ⌊u 1 ⌋ = 7, u 2 = 1 / u 1 − 7 ≈ 15.9966 and a 2 = ⌊u 2 ⌋ = 15, u 3 = 1 / u 2 − 15 ≈ 1.0034. Continuing like this, one can determine the infinite continued fraction of π as [3;7,15,1,292,1,1 ...
If x 2 is the remaining fraction after this step of the greedy expansion, it satisfies the equation P 1 (x 2 + 1 / 2 ) = 0, which can be expanded as P 2 (x 2) = 4x 2 2 + 8x 2 − 1 = 0. Since P 2 (x) < 0 for x = 1 / 9 , and P 2 (x) > 0 for all x > 1 / 8 , the next term in the greedy expansion is 1 / 9 .
The 142857 number sequence is also found in several decimals in which the denominator has a factor of 7. In the examples below, the numerators are all 1, however there are instances where it does not have to be, such as 2 / 7 (0. 285714). For example, consider the fractions and equivalent decimal values listed below: 1 / 7 = 0 ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The Dirty Fork, also known simply as Restaurant Sketch, is a Monty Python sketch that appeared in episode 3 of the first series of the television series Monty Python's Flying Circus, and later in the film, And Now For Something Completely Different.