The Greek Number Converter

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Enter an integer (up to 40 digits) and press “Enter.”

The « and » links subtract and add one from numbers up to 1,000,000,000,000,000.  After clicking the link, you can press the “Enter.” key to repeat it.  “HTML” toggles the Greek number to and from HTML.

This script converts modern Arabic numerals to the alphabetic (also referred to as the Ionian or Milesian) Greek number system.  Briefly, this was a decimal system that used letters to represent digits as shown above.  As it did not include zero, different letters were used to represent the ones, tens, and hundreds.  Our 27 would thus be written κζʹ.  The pattern repeated itself for thousands, with a different diacritical mark to indicate the change in magnitude.  However, for numbers greater than 9,999, the magnitude of the digits becomes ambiguous; so the letter M (for Μυριάς, a remnant of the older acrophonic system) was included to indicate multiplication by ten thousand, with the higher digits written above or beside it.

Note that three archaic letters, ϛ (digamma or stigma), ϙ (koppa), and ϡ (san or sampi) are used as digits, accompanied by the numeral signs ʹ and ͵.  Many Unicode Greek fonts are still missing some or all of these.  See if you need a font.

To my knowledge, this is the first script of its kind published on the internet.  Historically, there were variations on how the digits were represented, especially those over 9,999.  This rendering is based on the system proposed by Apollonius of Perga, described at The MacTutor History of Mathematics at the School of Mathematics and Statistics, University of St. Andrews, Scotland.  The digits are strung together in groups of four; an M preceeds the groups after the first, with an additional digit to indicate the power of the M.  Using only a single power digit, this script works for numbers through 9,999,999,999,999,999,999,999,999,999,999,999,999,999.  Partly because of limitations imposed by web page forms, I have modernized the rendering slightly by placing the power of the myriad beside, rather than above, the M; separating the groups by commas; and using the later convention of accent-like upper and lower numeral signs instead of an iota superscript.

For example:  2,056,839,184 becomes βΜκʹ, αΜ͵εχπγ, ͵θρπδ.
͵θρπδ represents the final 9184, ͵εχπγ the 5683, with αΜ indicating that the latter is multiplied by the first power of M (10,000).  βΜκʹ represents 20 multiplied by the second power of M (100,000,000).
Formatting the text can more closely approximate Apollonius’ representation:
βΜκ χαι αΜιεχπγ χαι ιθρπδ

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