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Trigonometry, in the form of a table of chord lengths in a circle, was probably used by Claudius Ptolemy of Alexandria to obtain the value of π given in the Almagest (circa 150 CE). [ 68 ] Advances in the approximation of π (when the methods are known) were made by increasing the number of sides of the polygons used in the computation.
The fraction 99 / 70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator. Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: [2]
Helium is the least water-soluble monatomic gas, [96] and one of the least water-soluble of any gas (CF 4, SF 6, and C 4 F 8 have lower mole fraction solubilities: 0.3802, 0.4394, and 0.2372 x 2 /10 −5, respectively, versus helium's 0.70797 x 2 /10 −5), [97] and helium's index of refraction is closer to unity than that of any other gas. [98]
The fraction of the total energy density of our (flat or almost flat) universe that is dark energy, , is estimated to be 0.669 ± 0.038 based on the 2018 Dark Energy Survey results using Type Ia supernovae [7] or 0.6847 ± 0.0073 based on the 2018 release of Planck satellite data, or more than 68.3% (2018 estimate) of the mass–energy density ...
The function: () = [/, /], shown on the figure at the right, satisfies all Kakutani's conditions, and indeed it has many fixed points: any point on the 45° line (dotted line in red) which intersects the graph of the function (shaded in grey) is a fixed point, so in fact there is an infinity of fixed points in this particular case.
The astronomical unit (symbol: au [1] [2] [3] [4] or AU) is a unit of length defined to be exactly equal to 149 597 870 700 m. [5] Historically, the astronomical unit ...
The elements between uranium and curium form a transition between these two kinds of behaviour, where higher oxidation states continue to exist, but lose stability with respect to the +3 state. [82] The +2 state becomes more important near the end of the series, and is the most stable oxidation state for nobelium, the last 5f element. [ 82 ]
In finance, the rule of 72, the rule of 70 [1] and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling.