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Cycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypad. Figure 1 is used for multiples of 1, 3, 7, and 9. Figure 2 is used for the multiples of 2, 4, 6, and 8. These patterns can be used to memorize the multiples of any number from 0 to 10, except 5.
In a third layer, the logarithms of rational numbers r = a / b are computed with ln(r) = ln(a) − ln(b), and logarithms of roots via ln n √ c = 1 / n ln(c).. The logarithm of 2 is useful in the sense that the powers of 2 are rather densely distributed; finding powers 2 i close to powers b j of other numbers b is comparatively easy, and series representations of ln(b) are ...
The ubiquity of γ revealed by the large number of equations below and the fact that γ has been called the third most important mathematical constant after π and e [37] [12] makes the irrationality of γ a major open question in mathematics. [2] [38] [39] [32]
The other is based on the distance and relative velocity of a series or "ladder" of different kinds of stars, making it depend on local measurements late in the history of the universe. [2] These two methods give slightly different values for the Hubble constant , which is then used in a formula to calculate the age.
For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.
37 is a prime number, [1] a sexy prime, and a Padovan prime 37 is the first irregular prime with irregularity index of 1. [ 2 ] 37 is the smallest non-supersingular prime in moonshine theory . 37 is also an emirp because it remains prime when its digits are reversed.
which can be rounded up to 2.646 to within about 99.99% accuracy (about 1 part in 10000); that is, it differs from the correct value by about 1 / 4,000 . The approximation 127 / 48 (≈ 2.645833...) is better: despite having a denominator of only 48, it differs from the correct value by less than 1 / 12,000 , or less than ...
Abundance (atom fraction) of the chemical elements in Earth's upper continental crust as a function of atomic number; [5] siderophiles shown in yellow Graphs of abundance against atomic number can reveal patterns relating abundance to stellar nucleosynthesis and geochemistry.