Greek numerals

Greek numerals are a system of representing numbers using letters of the Greek alphabet. In modern Greece, they are still in use for ordinal numbers, and in much the same situations as Roman numerals are in the West; for ordinary numbers, Arabic numerals are used.

Hellenistic zero

Hellenistic astronomers extended this into a sexagesimal positional numbering system by limiting each position to a maximum value of 50 + 9 and including a special symbol for 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 minutes, seconds, thirds, fourths, etc.)—they were not used for the 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 (c. 380), and Theon's daughter Hypatia (died 415).

Related Topics:
Hellenistic - Astronomer - Sexagesimal - Positional - Numbering system - Zero - Integral - Babylonian numerals - Hipparchus - 140 BC - Ptolemy - 140 - Theon - 380 - Hypatia - 415

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The Greek sexagesimal place holder or zero symbol changed over time. The symbol used on 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 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".

Related Topics:
Papyri - Second century - Byzantine

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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 eclipses) or the center of Earth's shadow (for lunar eclipses). 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.

Related Topics:
Moon - Sun - Solar eclipse - Earth - Lunar eclipse

~ ~ ~ ~ ~ ~ ~ ~ ~ ~