Constant (mathematics)

A fixed mathematical value that does not vary within a specified expression, function, or situation. Its constancy is relative to what is allowed to change.

Variable (mathematics): A symbol or quantity whose value can vary within a mathematical setting. A constant is fixed where a variable is allowed to change.
Constant of integration: An arbitrary additive constant introduced when an indefinite integral is taken. Differentiation erases additive constants, so integration must restore an undetermined one.
Euler's number: The irrational number approximately 2.71828 that is the base of the natural logarithm. It is a named constant central to exponential growth and calculus.
Identity element: An element that leaves other elements unchanged under a specified operation. An identity is defined by its effect in an operation, not by being unvarying.
Limit (mathematics): A value that a function or sequence approaches under a specified limiting process. A function may approach a constant without ever taking that value.
Parameter: A quantity held fixed within a calculation or model but allowed to vary between cases. Parameters expose how a constant can be fixed locally yet vary across a family of models.
Initial condition: A specified value of a solution or its derivatives at a chosen starting point. It can determine the otherwise free constant in a differential-equation solution.
Pi: The ratio of a circle's circumference to its diameter, approximately 3.14159. It is a geometric constant that appears in formulas for circles and periodic phenomena.
Identity function: The function that maps every element of a set to itself. Unlike a constant function, its output generally changes with its input.
Dimensional analysis: The study of physical quantities through their dimensions and units. It distinguishes dimensionless constants from constants carrying physical units.

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