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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.".
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• Greedy_algorithm_for_Egyptian_fractions wikiPageID "7277012".
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• Greedy_algorithm_for_Egyptian_fractions wikiPageRevisionID "588217984".
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink American_Journal_of_Mathematics.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink American_Mathematical_Monthly.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Ancient_Egyptian_mathematics.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Category:Egyptian_fractions.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Category:Integer_sequences.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Category:Number_theory.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Egyptian_fraction.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Egyptian_mathematics.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Engel_expansion.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Erdős–Straus_conjecture.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Fibonacci.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Fibonacci_number.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Golden_ratio.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Greedy_algorithm.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Group_theory.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Irrational_number.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Irreducible_fraction.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Leonardo_of_Pisa.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Liber_Abaci.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Mathematics.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Odd_greedy_expansion.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Perfect_number.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Rational_number.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Root-finding_algorithm.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Sylvesters_sequence.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLink Unit_fraction.
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLinkText "Greedy algorithm for Egyptian fractions".
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLinkText "Sylvester expansion".
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLinkText "greedy Egyptian expansion".
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLinkText "greedy algorithm for Egyptian fractions".
• Greedy_algorithm_for_Egyptian_fractions wikiPageWikiLinkText "greedy algorithm".
• 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".
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• Greedy_algorithm_for_Egyptian_fractions wikiPageUsesTemplate Template:Refend.
• 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 hypernym Algorithm.
• Greedy_algorithm_for_Egyptian_fractions type Software.
• Greedy_algorithm_for_Egyptian_fractions type Combinatoric.
• Greedy_algorithm_for_Egyptian_fractions type Field.
• Greedy_algorithm_for_Egyptian_fractions type Integer.
• 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 sameAs Sylvester-expansie.
• Greedy_algorithm_for_Egyptian_fractions sameAs m.025x_q_.
• Greedy_algorithm_for_Egyptian_fractions sameAs Жадный_алгоритм_для_египетских_дробей.
• Greedy_algorithm_for_Egyptian_fractions sameAs Похлепни_алгоритам_за_египатске_разломке.
• Greedy_algorithm_for_Egyptian_fractions sameAs Q5601712.
• Greedy_algorithm_for_Egyptian_fractions sameAs Q5601712.
• Greedy_algorithm_for_Egyptian_fractions wasDerivedFrom Greedy_algorithm_for_Egyptian_fractions?oldid=588217984.
• Greedy_algorithm_for_Egyptian_fractions isPrimaryTopicOf Greedy_algorithm_for_Egyptian_fractions.