There are no exact division algorithms for 3 or more players but there are'near exact'algorithms which are also envy-free and can achieve any desired degree of accuracy.
32.
Barbanel, Brams and Stromquist study the existence of divisions of a pie, which are both EQ and EF . The following existence results are proved without providing a specific division algorithm:
33.
A mathematical manual called " Sunzi mathematical classic " dated between 200 400 CE contained the most detailed step by step description of Sunzi division algorithm described in Sunzi mathematical classic four centuries earlier.
34.
Also, consider the software and papers of David M . Smith, especially the paper " A Multiple-Precision Division Algorithm " .-- T 23 : 27, 23 June 2006 ( UTC)
35.
The theorem is frequently referred to as the " division algorithm ", although it is a theorem and not an algorithm, because its proof as given below also provides a simple division algorithm for computing and.
36.
The theorem is frequently referred to as the " division algorithm ", although it is a theorem and not an algorithm, because its proof as given below also provides a simple division algorithm for computing and.
37.
A simple example of an output-sensitive algorithm is given by the division algorithm " division by subtraction " which computes the quotient and remainder of dividing two positive integers using only addition, subtraction, and comparisons:
38.
Quote notation s arithmetic algorithms work with a typical right-to-left direction, in which the addition, subtraction, and multiplication algorithms have the same complexity for natural numbers, and division is easier than a typical division algorithm.
39.
A useful benefit of including this instruction is that it allows an efficient software implementation of division ( see division algorithm ) and square root ( see methods of computing square roots ) operations, thus eliminating the need for dedicated hardware for those operations.
40.
The Sunzi algorithm for division was transmitted in toto by al Khwarizmi to Islamic country from Indian sources in 825AD . Al Khwarizmi's book was translated into Latin in the 13th century, The Sunzi division algorithm later evolved into Galley division in Europe.
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