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For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical ...
For example, German mathematician Ludolph van Ceulen of the 16th century spent a major part of his life calculating the first 35 digits of pi. [22] Using computers and supercomputers , some of the mathematical constants, including π, e , and the square root of 2, have been computed to more than one hundred billion digits.
[1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4] Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
For example, the speed of light is defined as having the numerical value of 299 792 458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a ...
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43), where he described it as "worthy of serious consideration". [2] [3] Euler initially calculated the constant's value to 6 decimal places. In 1781, he calculated it to 16 decimal places.
For example, the function y(x) = 4 is the specific constant function where the output value is c = 4. The domain of this function is the set of all real numbers. The image of this function is the singleton set {4}. The independent variable x does not appear on the right side of the function expression and so its value is "vacuously substituted ...