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Sunday, November 21, 2010

Glyphs: The shapes and forms of our numerals

To see the evolution of our numbers, especilly our zero see our other post.

The form of the numerals in the west of the Arabic empire look more familiar to those using European numerals today which is not surprising since it is from these numerals that the Indian number system reach Europe.

al-Banna al-Marrakushi's form of the numerals
He gave this form of the numerals in his practical arithmetic book written around the beginning of the fourteenth century. He lived most of his life in Morocco which was in close contact with al-Andalus, or Andalusia, which was the Arab controlled region in the south of Spain.

La divisione secondo il metodo "per galera",
derivata da quella con l'abaco (utilizzata fino a secolo XV)

But in the north of Spain we have the figure of Gerbert:

Gerbert compiled a list of rules for computing with his abacus, Regula de Abaco Computi, in which he painstakingly explained how to multiply and divide, as well as add and subtract, in the new system.  A companion work, Liber Abaci, by his student Bernelin, is often included in the collected works of Gerbert; it predates the book of the same name by Fibonacci by two hundred years. 

A history of mathematical notations, byFlorian Caiori (1928):

"The forms varied considerably. the number five was the most freakish. An upright 7 was rare in the earlier centuries. The symbol for
zero (0) of the XII and XIII centuries i is sometimes crossed 
by a horizontal line, or a line slanting upward.  The Boethian apices, 
as found in some manuscripts, contain a triangle inscribed in the 
circular zero. In Athelard of Bath's translation of Al-Madjrltl's re- 
vision of Al-Khowarizmi's astronomical tables there are in different 
manuscripts three signs for zero,  namely the Greek letters (Θ = theta?) referred 
to above, then T ( = theca, teca),* and 0 with a bar on top (0).

see David E. Smith History of mathematics-I)

to see the evolution of the figures, we pay attention to number, glyph, 5.
   The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Kushana and Gupta Indians had among themselves several different glyphs which bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5

see the full list between 976-XIII below:

For a wider set (976-XVI) see G. F. Hill The Development of Arabic numerals

The familiar shape (see wapedia) of the Western Arabic glyphs as now used with the Latin alphabet, (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they enter earlytypesetting. Muslim scientists used the Babylonian numeral system, and merchants used the Abjad numerals, a system similar to the Greek numeral system and the Hebrew numeral system. Similarly, Fibonacci's introduction of the system to Europe was restricted to learned circles. The credit of first establishing widespread understanding and usage of the decimal positional notation among the general population goes to Adam Ries, an author of the German Renaissance, whose 1522 Rechenung auff der linihen und federn was targeted at the apprentices of businessmen and craftsmen.

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