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Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
[1] [4] [33] To elaborate, in trying to find the length of a wavy non-fractal curve, one could find straight segments of some measuring tool small enough to lay end to end over the waves, where the pieces could get small enough to be considered to conform to the curve in the normal manner of measuring with a tape measure. But in measuring an ...
The convergents of the continued fraction for φ are ratios of successive Fibonacci numbers: φ n = F n+1 / F n is the n-th convergent, and the (n + 1)-st convergent can be found from the recurrence relation φ n+1 = 1 + 1 / φ n. [31] The matrix formed from successive convergents of any continued fraction has a determinant of +1 or −1.
The Avogadro constant, commonly denoted N A [1] or L, [2] is an SI defining constant with an exact value of 6.022 140 76 × 10 23 mol −1 (reciprocal moles). [3] [4] It is this defined number of constituent particles (usually molecules, atoms, ions, or ion pairs—in general, entities) per mole and used as a normalization factor in relating the amount of substance, n(X), in a sample of a ...
The formula above is obtained by combining the composite Simpson's 1/3 rule with the one consisting of using Simpson's 3/8 rule in the extreme subintervals and Simpson's 1/3 rule in the remaining subintervals. The result is then obtained by taking the mean of the two formulas.
Sigma (/ ˈ s ɪ ɡ m ə / SIG-mə; [1] uppercase Σ, lowercase σ, lowercase in word-final position ς; Ancient Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation.
Acetone (2-propanone or dimethyl ketone) is an organic compound with the formula (CH 3) 2 CO. [22] It is the simplest and smallest ketone (>C=O).It is a colorless, highly volatile, and flammable liquid with a characteristic pungent odour, very reminiscent of the smell of pear drops.