If you notice from these images taken from the powerpoint, the whole argument about angles being the source of the numeral system gets mighty tenuous when you get above 4, and makes no sense at all by the time you get to 9.
Click on the pictures for larger versionsIt turns out that angles didn’t have anything to do with it. The original numerals, since they were hand-written, didn’t have many angles at all.
Our Arabic numerals actually have an Indian Hindu origin, not Arab. I am not sure why the Arabs get credit for such things. Their mathematics and astronomy were all copied from Brahmagupta's Brahmasphutasiddhanta (The Opening of the Universe) which was written in 628 AD, including the number zero, trigonometry etc. All Indian, not Arab.
Here are the original Brahmi numerals from 1st-century India:
The first Arabic-Hindi numerals in Europe appeared in the Codex Vigilanus in the year 976:
Here is Montucla’s Table from 1757 showing early European variants taken from various manuscripts/authors which are shown in the left column. Interesting that 7 and 8 are the blade and chalice :
And here are some more variations in early European works, possibly also from Montucla. People pretty much made up their own personal notations – as they did with spelling:
Even in the 15th century, numbers were very recognizable. These are off the World Map from Ptolemy, Cosmographia. Ulm: Lienhart Holle, 1482:
Standardized Arabic-Hindu notation really took off with the invention of movable type by J. Gutenburg in 1450. I remember seeing numerous examples in the Gutenburg Museum in Mainz – which is a very interesting place to visit if you have a chance.
(A poem was actually the first full-page item printed if I remember correctly. Most of the stuff printed was for merchants, and also enormous numbers of indulgences for the church. The Bibles were printed starting several years later).
Here is a table of modern variants:
The poor Tamils evidently still don’t have a zero.
Finally, here is a telephone keypad from Egypt showing both European “Arabic” numerals and Eastern Arabic numerals:
I note that 9's with curlicue tails and crossed 7's don't appear at all in these ancient systems. Why our numbers look the way they do is still unknown, but is likely attributable to creative folks making small changes that they simply liked better, and set them apart from others -- like a signature.
It is interesting that printing, as well as standardization of handwriting and spelling, has created a world that labels people who make such creative changes as uneducated dolts. I would have a hard time using unique and creative numerals on this blog, but pur happs I mite do a littel creativ spellen.