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Approximation: An approximation is anything that is intentionally similar but not exactly equal to something else.
Approximation algorithm: In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture.
Approximations of π: Approximations for the mathematical constant pi in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.
Approximation theory: In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on the application.