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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed. Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ...
Wikimedia Commons has media related to: Science For the scientific journal named Science, see Science (journal). ...
In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ...
Unspecified constants
The most widely mentioned sort of constant is a fixed, but possibly unspecified, number. Usually the term constant is used in connection with mathematical functions of one or more variable arguments. These arguments, or other variables, are often called x, y, or z, using lower-case letters from the end of the English alphabet. Constants are by convention usually denoted by lower-case letters from the beginning of the English alphabet, such as a, b, and c. Number is the current mathematics collaboration of the week! Please help improve it to featured article standard. ...
Partial plot of a function f. ...
In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ...
A parameter is a measurement or value on which something else depends. ...
The English language has been written using the Latin alphabet from ca. ...
Specified constants Of course, some constants have special symbols, because they are specified, such as 1 or π. Look up one in Wiktionary, the free dictionary. ...
Lower-case pi The mathematical constant Ï€ is a real number which is defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
A special case of this may be found in physics, chemistry, and related fields, where certain features of the natural world that are described by numbers are found to have the same value at all times and places. A Superconductor demonstrating the Meissner Effect Physics (from the Greek, φυσικός (physikos), natural, and φÏσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ...
Chemistry (derived from the Arabic word kimia, alchemy, where al is Arabic for the) is the science that deals with the properties of organic and inorganic substances and their interactions with other organic and inorganic substances. ...
For example, in Albert Einstein's special theory of relativity, we have the formula The factual accuracy of this article is disputed. ...
Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ...
In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
- E=mc².
Here, the letter c stands for the speed of light in a vacuum, which is the same in all physical situations (to the best of current knowledge). In contrast, the letter m stands for the mass of an object, which could be anything, so it is a variable. E stands for the object's rest energy, another variable, and the formula defines a function that gives rest energy in terms of mass. The theoretical physics equation E = mc2 states a relationship between energy (E), in whatever form, and mass (m). ...
Cherenkov effect in a swimming pool nuclear reactor. ...
For other uses, see vacuum cleaner and Vacuum (musical group). ...
Mass is a property of a physical object that quantifies the amount of matter it contains. ...
Partial plot of a function f. ...
- (See mathematical constant and physical constant.)
A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ...
In science, a physical constant is a physical quantity whose numerical value does not change. ...
Constant term A constant term is a number that appear as an addend in a formula, such as Addition is one of the basic operations of arithmetic. ...
In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
- f(x) = sinx + c.
Here the constant c is the constant term of the function f. The value of c has not been specified in this formula, but it must be a specific value for f to be a specific function. Partial plot of a function f. ...
The constant term may depend on how the formula is written. For example
- f(x) = x3 + (sinx)2 + 4
and - g(x) = x3 − (cosx)2 + 5
are formulae for the same function.
In a polynomial (or a generalisation of a polynomial, such as a Taylor series or Fourier expansion), the constant term is associated to the exponent zero. Note that the constant term may be zero, however. In a sense, any formula has a constant term, if you allow the constant term to be zero. In mathematics, a polynomial is an expression in which constants and powers of variables are combined using (only) addition, subtraction, and multiplication. ...
As the degree of the Taylor series rises, it approaches the correct function. ...
In mathematics, a Fourier series, named in honor of Joseph Fourier (1768-1830), is a representation of a periodic function (often taken to have period 2π — in a sense, the simplest case) as a sum of periodic functions of the form which are harmonics of ei x. ...
In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ...
0 (zero), alternatively called naught, nil, nada, ought zilch, zip, nothing or nought, is both a number and a numeral. ...
For some purposes, the constant is taken to be the value of f(0), but this depends on the function being defined at 0; it would not work for f(x)=1-1/x.
Constants vs variables A number that is constant in one place may be a variable in another. Consider the example above, with a function f defined by Partial plot of a function f. ...
- f(x) = sin x + c.
Now consider a functional F, a function whose argument is itself another function, defined by In mathematics, the term functional is applied to certain functions. ...
- F(g) = g(π/2).
Then for the function f given above, we have - F(f) = c + 1.
In the formula for f(x), we are fixing c and varying x, so c is a constant. But in the formula for F(f), we are varying both c and f, so c is a variable. Even this statement might be false in the presence of some larger context that gives yet another point of view.
Thus, there is no precise definition of "constant" in mathematics; only phrases such as "constant function" or "constant term of a polynomial" can be defined. A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between one expression and another, usually more complex expression that gives the meaning of the first. ...
There is a mathematicians' joke to the effect that "variables don't; constants aren't." That is, the term variable is frequently used to mean a value that is fixed in a given equation, albeit unknown; while the term constant is used to mean an arbitrary quantity which may assume any value, as in the constant of integration. This article is in need of attention from an expert on the subject. ...
Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ...
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