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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1] For example, the constant π may be defined as the ratio of the length of a circle's circumference to ...
The derivative of a constant function is zero, as noted above, and the differential operator is a linear operator, so functions that only differ by a constant term have the same derivative. To acknowledge this, a constant of integration is added to an indefinite integral ; this ensures that all possible solutions are included.
In certain cases, algorithms or other methods exist for proving that a given expression is non-zero, or of showing that the problem is undecidable. For example, if x 1, ..., x n are real numbers, then there is an algorithm [2] for deciding whether there are integers a 1, ..., a n such that
Apéry's constant arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio, computed using quantum electrodynamics. [ 9 ] ζ ( 3 ) {\displaystyle \zeta (3)} is known to be an irrational number which was proven by the French mathematician Roger Apéry in 1979.
6174 is known as Kaprekar's constant [1] [2] [3] after the Indian mathematician D. R. Kaprekar.This number is renowned for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).
As an example, starting with the number 8991 in base 10: 9981 – 1899 = 8082 8820 – 0288 = 8532 8532 – 2358 = 6174 7641 – 1467 = 6174. 6174, known as Kaprekar's constant, is a fixed point of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. [3]
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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.