« Grec ancien/Numération » : différence entre les versions

ins de sables
(ins de sables)
{{Numération}}
 
La '''numération grecque''' de l'[[Antiquité]] était double : on pouvait écrire les chiffres et les nombres soit au moyen de signes dits « acrophoniques » parce qu'ils représentaient ''grosso modo'' la première lettre de leur nom en [[grec ancien]] soit par des lettres, comme la [[numération hébraïque]] ou [[numération arabe|arabe]]. On connait également un système de numération ''scientifique'', inspiré des [[mathématiques babyloniennes]]. Actuellement, ce sont les [[chiffres arabes]] que l'on utilise le plus fréquemment en Grèce.
 
==Numération acrophonique==
==Numération alphabétique==
Ce système existe encore aujourd'hui en [[Grèce]], à la manière des [[numération romaine|chiffres romains]] dans les pays de [[langues romanes]]. Elle utilise, outre les lettres courantes de l'[[alphabet grec]], trois [[lettres étendues de l'alphabet grec|lettres archaïques]], ''[[digamma]]'' (tracé le plus souvent comme un ''[[stigma]]''), ''[[koppa]]'' (distinct du ''koppa'' littéral ancien) et ''[[sampi]]'' (évolution d'une lettre plus ancienne). Purement additive, cette numération ne nécessite pas l'utilisation du [[zéro]]. Cependant, le calcul basé sur ces écritures est impossible : les anciens Grecs utilisaient des jetons placés sur des [[abaque (calcul)|abaque]]s, de bois ou de marbre, partagés en colonnes.
 
==Numération ''scientifique''==
Outre la [[myriade]] (M') représentant dix mille (<math>10^4</math>), on connait aussi des exemples de myriade de myriades (MM') pour représenter cent millions (<math>10^8</math>). Dans [[l'Arénaire]], [[Archimède]] proposa des méthodes plus élaborées (proches de notre moderne [[notation scientifique]] pour nommer de très grands nombres comme celui des grains de sable sur une plage, ou celui des gra.
 
==Hellenistic zero==<!-- This section is linked from [[Number]] -->
[[Hellenistic civilization|Hellenistic]] [[astronomer]]s extended alphabetic Greek numerals into a [[sexagesimal]] [[positional notation|positional]] [[numeral system|numbering system]] by limiting each position to a maximum value of 50 + 9 and including a special symbol for [[0 (number)|zero]], which was also used alone like our modern zero, more than as a simple placeholder. However, the positions were usually limited to the fractional part of a number (called [[minute]]s, seconds, thirds, fourths, etc.) — they were not used for the [[integer|integral]] part of a number. This system was probably adapted from [[Babylonian numerals]] by [[Hipparchus]] c. [[140 BC]]. It was then used by [[Ptolemy]] (c. [[140]]), [[Theon of Alexandria|Theon]] (c. [[380]]), and Theon's daughter [[Hypatia of Alexandria|Hypatia]] (died [[415]]).
 
The Greek sexagesimal place holder or zero symbol changed over time. The symbol used on [[papyrus|papyri]] during the [[second century]] was a very small circle with an overbar several diameters long, terminated or not at both ends in various ways. Later, the overbar shortened to only one diameter, similar to our modern o macron (ō) which was still being used in late medieval Arabic manuscripts whenever alphabetic numerals were used. But the overbar was omitted in [[Byzantine Empire|Byzantine]] manuscripts, leaving a bare ο (omicron). This gradual change from an invented symbol to ο does not support the hypothesis that the latter was the initial of ουδεν meaning "nothing".<ref>Otto Neugebauer, ''The Exact Sciences in Antiquity'' (second edition, Providence, RI: Brown University Press, 1957) 13-14, plate 2.</ref><ref>Raymond Mercier, {{pdflink|[http://anubis.dkuug.dk/JTC1/SC2/WG2/docs/n2708.pdf Consideration of the Greek symbol 'zero']|1.31MB}} Numerous examples</ref>
 
Some of Ptolemy's true zeros appeared in the first line of each of his eclipse tables, where they were a measure of the angular separation between the center of the [[Moon]] and either the center of the [[Sun]] (for [[solar eclipse]]s) or the center of [[Earth]]'s shadow (for [[lunar eclipse]]s). All of these zeros took the form 0 | 0 0, where Ptolemy actually used three of the symbols described in the previous paragraph. The vertical bar (|) indicates that the integral part on the left was in a separate column labeled in the headings of his tables as ''digits'' (of five arc-minutes each), whereas the fractional part was in the next column labeled ''minutes of immersion'', meaning sixtieths (and thirty-six-hundredths) of a digit.<ref>''Ptolemy's [[Almagest]]'', translated by G. J. Toomer, Book VI, (Princeton, NJ: Princeton University Press, 1998), pp.306-7.</ref>
 
 
 
 
 
===Histoire===
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