Constant (mathematics)

In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings:

For a narrower treatment related to this subject, see Mathematical constant.

For example, a general quadratic function is commonly written as:

where $a$ , $b$ and $c$ are constants (coefficients or parameters), and $x$ a variable—a placeholder for the argument of the function being studied. A more explicit way to denote this function is

which makes the function-argument status of $x$ (and by extension the constancy of $a$ , $b$ and $c$ ) clear. In this example $a$ , $b$ and $c$ are coefficients of the polynomial. Since $c$ occurs in a term that does not involve $x$ , it is called the constant term of the polynomial and can be thought of as the coefficient of $x 0$ . More generally, any polynomial term or expression of degree zero (no variable) is a constant.^[3]^: 18

0 ().

zero

1 (), the natural number after zero.

one

$π$ (), the constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.141592653589793238462643.^[6]

pi

, approximately equal to 2.718281828459045235360287.^[7]

e

$i$ , the such that $i 2 = -1$ .^[8]

imaginary unit

${\sqrt {2}}$ (), the length of the diagonal of a square with unit sides, approximately equal to 1.414213562373095048801688.^[9]

square root of 2

$φ$ (), approximately equal to 1.618033988749894848204586, or algebraically, $1+{\sqrt {5}} \over 2$ .^[10]

golden ratio

Some values occur frequently in mathematics and are conventionally denoted by a specific symbol. These standard symbols and their values are called mathematical constants. Examples include:

Constant (mathematics)

zero

one

pi

e

imaginary unit

square root of 2

golden ratio

Constant (disambiguation)

Expression

Level set

List of mathematical constants

Physical constant