Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero
| Autor: | Julyan H. E. Cartwright, Diego L. González, Costanza Rangoni, Berenice Rojo-Garibaldi |
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| Rok vydání: | 2021 |
| Předmět: |
0301 basic medicine
Computer science History and Overview (math.HO) Number representation systems 03 medical and health sciences 0302 clinical medicine Development (topology) Redundancy (engineering) FOS: Mathematics Arithmetic lcsh:Social sciences (General) Mesoamerican Long Count calendar lcsh:Science (General) Bijective numeration Multidisciplinary Mathematics - History and Overview Vigesimal Pre-Columbian Mesoamerica Zero Zero (linguistics) 030104 developmental biology Maya Olmec Positional notation lcsh:H1-99 030217 neurology & neurosurgery Research Article lcsh:Q1-390 |
| Zdroj: | Heliyon, Vol 7, Iss 3, Pp e06580-(2021) Digibug: Repositorio Institucional de la Universidad de Granada Universidad de Granada (UGR) Heliyon Digital.CSIC. Repositorio Institucional del CSIC instname Digibug. Repositorio Institucional de la Universidad de Granada |
| Popis: | Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 × 20, …, 18 × 20n. We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems. Zero; Maya; Pre-Columbian Mesoamerica; Number representation systems; Bijective numeration |
| Databáze: | OpenAIRE |
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