Counting Number Angles

Date: 10/13/2002 at 13:25:53
From: Terri R
Subject: Counting Number Angles

I am trying to find the history of counting number angles. I was told 
by my professor that the way the numbers were written gave you the 
number in the number of angles in the written number, such as the 
number 2 being written as what we know as a Z: there are two angles 
in this number, meaning it is the number 2. Can you give me more 
information on this type of math history?

Date: 10/13/2002 at 23:42:35
From: Doctor Peterson
Subject: Re: Counting Number Angles

Hi, Terri.

In Cajori's _A History of Mathematical Notations_ (p. 65), there is a 
chart showing "Fanciful hypotheses on the origin of the numeral 
forms." One of these (II) suggests that the numerals originated as 
various numbers of dots, which were connected with lines; another (V) 
shows various numbers of angles as you describe:
        __  __       _   _   _   __   _
    /|   /   /  \/  |_  |_  ' /  \/  |_|_
     |  /_  _\  /\  ,_| |_| _|_  /\  ,_|
                             |

Cajori says, "A French writer, P. Voizot, entertained the theory that 
originally a numeral contained as many angles as it represents units, 
as seen in Part V. He did not claim credit for this explanation, but 
ascribed it to a writer in the Genova Catholico Militarite. But 
Voizot did originate a theory of his own, based on the number of 
strokes, as shown in Part VI."
       __   __    __    __    __    __
    |    |    |  |  |  |__   |__   |__|  /\  /\
    |    |  __|  |__|   __|  |__|  |__|  \/  \/
                                         /\  /\
                                         \/  \/
                                             /

These are all entirely imaginary explanations of the origin of the 
symbols. It is not math history. To read about how they really 
originated, see the article at the MacTutor History of Mathematics 
archive at St. Andrews University:

The Arabic numeral system
http://www-history.mcs.st-and.ac.uk/HistTopics/Arabic_numerals.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/