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Machin-like formulas for π can be constructed by finding a set of integers , =, where all the prime factorisations of + , taken together, use a number of distinct primes , and then using either linear algebra or the LLL basis-reduction algorithm to construct linear combinations of arctangents of . For example, in the Størmer formula ...
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In other array types, a slice can be replaced by an array of different size, with subsequent elements being renumbered accordingly – as in Python's list assignment A[5:5] = [10,20,30], that inserts three new elements (10, 20, and 30) before element "A[5]".
Python supports most object oriented programming (OOP) techniques. It allows polymorphism, not only within a class hierarchy but also by duck typing. Any object can be used for any type, and it will work so long as it has the proper methods and attributes. And everything in Python is an object, including classes, functions, numbers and modules.
The BBP formula gives rise to a spigot algorithm for computing the nth base-16 (hexadecimal) digit of π (and therefore also the 4nth binary digit of π) without computing the preceding digits. This does not compute the n th decimal digit of π (i.e., in base 10). [ 3 ]
When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer. Indexes are also called subscripts. An index maps the array value to a stored object. There are three ways in which the elements of an array can be indexed: 0 (zero-based indexing)
Simon Plouffe (born June 11, 1956) is a French Canadian mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the nth binary digit of π, in 1995. [1] [2] [3] His other 2022 formula allows extracting the nth digit of π in decimal. [4] He was born in Saint-Jovite, Quebec.
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.