The unknown heritage is the name usually given to a problem type in whose archetype a father leaves to his first son 1 monetary unit and $${\frac{1}{n}}$$ (n usually being 7 or 10) of what remains, to the second 2 units and $${\frac{1}{n}}$$ of what remains, and so on. In the end, all sons get the same, and nothing remains. The earliest known occurrence is in Fibonacci's Liber abbaci, which also contains a number of much more sophisticated versions, together with a partial algebraic solution for one of these and rules for all which do not follow from his algebraic calculation. The next time the problem turns up is in Planudes's late thirteenth century Calculus according to the Indians, Called the Great. After that the simple problem type turns up regularly in Provençal, Italian and Byzantine sources. It seems never to appear in Arabic or Indian writings, although two Arabic texts (one from c. 1190) contain more regular problems where the number of shares is given; they are clearly derived from the type known from European and Byzantine works, not its source. The sophisticated versions turn up again in Barthélemy de Romans' Compendy de la praticque des nombres (c. 1467) and, apparently inspired from there, in the appendix to Nicolas Chuquet's Triparty (1484). Apart from a single trace in Cardano's Practica arithmetice et mensurandi singularis, the sophisticated versions never surface again, but the simple version spreads for a while to German practical arithmetic and, more persistently, to French polite recreational mathematics. Close examination of the texts shows that Barthélemy cannot have drawn his familiarity with the sophisticated rules from Fibonacci. It also suggests that the simple version is originally either a classical, strictly Greek or Hellenistic, or a medieval Byzantine invention; and that the sophisticated versions must have been developed before Fibonacci within an environment (located in Byzantium, Provence, or possibly in Sicily?) of which all direct traces has been lost, but whose mathematical level must have been quite advanced.
...MoreDescription On the lineage of a type of mathematical problem first associated with Fibonacci (Leonardo da Pisa).
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Conventions for Recreational Problems in Fibonacci's Liber Abbaci
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Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles
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An Early Abridgement of Fibonacci's De practica geometrie
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Fibonacci, Leonardo;
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Fibonacci and the Abacus Schools in Italy. Mathematical Conceptual Streams - Education and its Changing Relationship with Society
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Enrico Giusti;
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The Sources of Leonardo Pisano and how he used them
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Quelques observations sur le lexique technique de la Practica Geometrie de Léonard de Pise, dit Fibonacci
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La géométrie de la mesure dans les traductions arabo-latines médiévales
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False Position in Leonardo of Pisa's Liber Abbaci
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Alcuin's Sequence
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Diophantine Equations in Leonardo of Pisa
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Some mathematical problems and algorithms in Fibonacci's “Liber abaci” similar to those in ancient China
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Keith Devlin;
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Congruent Numbers in the Tenth and in the Twentieth Century
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Spiesser, Maryonne;
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Problèmes linéaires dans le Compendy de la praticque des nombres de Barthélemy de Romans et Mathieu Préhoude (1471): Une approche nouvelle basée sur des sources proches du Liber abbaci de Léonard de Pise
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