Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles

Jens Høyrup

Revue d'histoire des mathématiques (2005)

  • Volume: 11, Issue: 1, page 23-56
  • ISSN: 1262-022X

Abstract

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Since long it has been regarded as an obvious fact in need of no argument that the mathematics of the Italian abbacus school was taken over from Leonardo Fibonacci’s Liber abbaci. What does look like an argument is that an abbacus book from the outgoing 13th century (apparently the earliest extant specimen) claims to be made “according to the opinion” of Fibonacci. Close analysis of the text reveals, however, that everything basic is independent of Fibonacci, while the indubitable borrowings from the Liber abbaci are sophisticated matters, often copied without understanding; a text which appears to be copied from an even earlier treatise is wholly independent of Fibonacci but related to writings of abbacus type from the Ibero-Provençal area. Combination of the Italian and Ibero-Provençal evidence with certain passages in the Liber abbaci shows that the beginnings of abbacus mathematics must be traced to an environment that already existed in Fibonacci’s days – an environment he knew about and of which he can be regarded an extraordinary early exponent, but no founding father.

How to cite

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Høyrup, Jens. "Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles." Revue d'histoire des mathématiques 11.1 (2005): 23-56. <http://eudml.org/doc/252091>.

@article{Høyrup2005,
abstract = {Since long it has been regarded as an obvious fact in need of no argument that the mathematics of the Italian abbacus school was taken over from Leonardo Fibonacci’s Liber abbaci. What does look like an argument is that an abbacus book from the outgoing 13th century (apparently the earliest extant specimen) claims to be made “according to the opinion” of Fibonacci. Close analysis of the text reveals, however, that everything basic is independent of Fibonacci, while the indubitable borrowings from the Liber abbaci are sophisticated matters, often copied without understanding; a text which appears to be copied from an even earlier treatise is wholly independent of Fibonacci but related to writings of abbacus type from the Ibero-Provençal area. Combination of the Italian and Ibero-Provençal evidence with certain passages in the Liber abbaci shows that the beginnings of abbacus mathematics must be traced to an environment that already existed in Fibonacci’s days – an environment he knew about and of which he can be regarded an extraordinary early exponent, but no founding father.},
author = {Høyrup, Jens},
journal = {Revue d'histoire des mathématiques},
keywords = {Leonardo Fibonacci; abbacus mathematics; ibero-provençal practical arithmetic},
language = {eng},
number = {1},
pages = {23-56},
publisher = {Société mathématique de France},
title = {Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles},
url = {http://eudml.org/doc/252091},
volume = {11},
year = {2005},
}

TY - JOUR
AU - Høyrup, Jens
TI - Leonardo Fibonacci and Abbaco Culture. A Proposal to Invert the Roles
JO - Revue d'histoire des mathématiques
PY - 2005
PB - Société mathématique de France
VL - 11
IS - 1
SP - 23
EP - 56
AB - Since long it has been regarded as an obvious fact in need of no argument that the mathematics of the Italian abbacus school was taken over from Leonardo Fibonacci’s Liber abbaci. What does look like an argument is that an abbacus book from the outgoing 13th century (apparently the earliest extant specimen) claims to be made “according to the opinion” of Fibonacci. Close analysis of the text reveals, however, that everything basic is independent of Fibonacci, while the indubitable borrowings from the Liber abbaci are sophisticated matters, often copied without understanding; a text which appears to be copied from an even earlier treatise is wholly independent of Fibonacci but related to writings of abbacus type from the Ibero-Provençal area. Combination of the Italian and Ibero-Provençal evidence with certain passages in the Liber abbaci shows that the beginnings of abbacus mathematics must be traced to an environment that already existed in Fibonacci’s days – an environment he knew about and of which he can be regarded an extraordinary early exponent, but no founding father.
LA - eng
KW - Leonardo Fibonacci; abbacus mathematics; ibero-provençal practical arithmetic
UR - http://eudml.org/doc/252091
ER -

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