❪𝛿₁ₐ❫ Constants ○ Entries

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Constant ○꠹｜Definition｜1st｜20251119205401-00-⌔

Mathematical constant - Wikipedia

Mathematical constant

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A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians’ names to facilitate using it across multiple mathematical problems.¹ Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, statistics, and calculus.

Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (π). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places.

All named mathematical constants are definable numbers, and usually are also computable numbers (Chaitin’s constant being a significant exception).

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Footnotes

1. Weisstein, Eric W. “Constant”. mathworld.wolfram.com. Retrieved 2020-08-08. ↩

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❪𝛿₁ₐ❫ Constants ○｜Definition｜1st｜20251122125432-00-⌔

Constant (mathematics) - Wikipedia

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:

• A fixed and well-defined number or other non-changing mathematical object, or the symbol denoting it.¹² 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, a general quadratic function is commonly written as $a{x}^2+bx+c$, 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 $x\mapsto a{x}^2+bx+c$, 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.⁵${}^{:18}$

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Footnotes

1. Sobolev, S. K. (December 20, 2015) [1994]. “Constant”. Encyclopedia of Mathematics. EMS Press. ↩

2. Sobolev, S. K. (July 2, 2024) [1994]. “Individual constant”. Encyclopedia of Mathematics. EMS Press. ↩

3. “Definition of CONSTANT”. www.merriam-webster.com. Retrieved 2021-11-09. ↩

4. Weisstein, Eric W. “Constant”. MathWorld. ↩

5. Foerster, Paul A. (2006). Algebra and Trigonometry: Functions and Applications, Teacher’s Edition (Classics ed.). Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-165711-9. ↩

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