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- Greedy_algorithm_for_Egyptian_fractions abstract "In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of unit fractions, as e.g. 5/6 = 1/2 + 1/3. As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions is described in the Liber Abaci (1202) of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction.Fibonacci actually lists several different methods for constructing Egyptian fraction representations (Sigler 2002, chapter II.7). He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. As Salzer (1948) details, the greedy method, and extensions of it for the approximation of irrational numbers, have been rediscovered several times by modern mathematicians, earliest and most notably by J. J. Sylvester (1880); see for instance Cahen (1891) and Spiess (1907). A closely related expansion method that produces closer approximations at each step by allowing some unit fractions in the sum to be negative dates back to Lambert (1770).The expansion produced by this method for a number x is called the greedy Egyptian expansion, Sylvester expansion, or Fibonacci–Sylvester expansion of x. However, the term Fibonacci expansion usually refers, not to this method, but to representation of integers as sums of Fibonacci numbers.".
- Greedy_algorithm_for_Egyptian_fractions wikiPageExternalLink search?q=Egyptian-fraction-for.
- Greedy_algorithm_for_Egyptian_fractions wikiPageExternalLink search?q=greedy-Egyptian-fraction-expansion.
- Greedy_algorithm_for_Egyptian_fractions wikiPageID "7277012".
- Greedy_algorithm_for_Egyptian_fractions wikiPageRevisionID "588217984".
- Greedy_algorithm_for_Egyptian_fractions authorlink "James Joseph Sylvester".
- Greedy_algorithm_for_Egyptian_fractions first "J. J.".
- Greedy_algorithm_for_Egyptian_fractions hasPhotoCollection Greedy_algorithm_for_Egyptian_fractions.
- Greedy_algorithm_for_Egyptian_fractions last "Sylvester".
- Greedy_algorithm_for_Egyptian_fractions year "1880".
- Greedy_algorithm_for_Egyptian_fractions subject Category:Egyptian_fractions.
- Greedy_algorithm_for_Egyptian_fractions subject Category:Integer_sequences.
- Greedy_algorithm_for_Egyptian_fractions subject Category:Number_theory.
- Greedy_algorithm_for_Egyptian_fractions type Abstraction100002137.
- Greedy_algorithm_for_Egyptian_fractions type Arrangement107938773.
- Greedy_algorithm_for_Egyptian_fractions type Chemical114806838.
- Greedy_algorithm_for_Egyptian_fractions type EgyptianFractions.
- Greedy_algorithm_for_Egyptian_fractions type Fraction114922107.
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- Greedy_algorithm_for_Egyptian_fractions type IntegerSequences.
- Greedy_algorithm_for_Egyptian_fractions type Material114580897.
- Greedy_algorithm_for_Egyptian_fractions type Matter100020827.
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- Greedy_algorithm_for_Egyptian_fractions comment "In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of unit fractions, as e.g. 5/6 = 1/2 + 1/3.".
- Greedy_algorithm_for_Egyptian_fractions label "Greedy algorithm for Egyptian fractions".
- Greedy_algorithm_for_Egyptian_fractions label "Sylvester-expansie".
- Greedy_algorithm_for_Egyptian_fractions sameAs Sylvester-expansie.
- Greedy_algorithm_for_Egyptian_fractions sameAs m.025x_q_.
- Greedy_algorithm_for_Egyptian_fractions sameAs Q5601712.
- Greedy_algorithm_for_Egyptian_fractions sameAs Q5601712.
- Greedy_algorithm_for_Egyptian_fractions sameAs Greedy_algorithm_for_Egyptian_fractions.
- Greedy_algorithm_for_Egyptian_fractions wasDerivedFrom Greedy_algorithm_for_Egyptian_fractions?oldid=588217984.
- Greedy_algorithm_for_Egyptian_fractions isPrimaryTopicOf Greedy_algorithm_for_Egyptian_fractions.