Article ID: CBB001201186

Epistemic Justification and Operational Symbolism (2014)

unapi

By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280--1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of mathematical practices necessary for the development towards symbolic reasoning. It is shown how justification schemes compensated for the lack of symbolism in abbaco treatises and at the same time facilitated a process of abstraction.

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Description On the methods of calculating with Hindu-Arabic numerals in what is known as the Abbaco period, which flourished during 1280--1500.


Citation URI
https://data.isiscb.org/isis/citation/CBB001201186/

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Authors & Contributors
Iqbal, Muzaffar
Pfeiffer, Judith
Hauko Wakabayashi
Kenneth R. Robinson
Rabii, Maryam
Weill-Parot, Nicolas
Concepts
Mathematics
Arab/Islamic world, civilization and culture
Transmission of ideas
Cross-cultural interaction; cultural influence
Astronomy
Algorithms
Time Periods
14th century
13th century
15th century
Medieval
12th century
Ancient
Places
Europe
Mediterranean region
China
Tabrīz (Iran)
Middle and Near East
Pisa (Italy)
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