Ancient Math Symbols

Date: 09/07/97 at 10:43:21
From: Carly Siegel
Subject: Ancient math symbols

I need to know the numerals for 1,10 100, 1000 in Arab, Sumarian, 
Greek, Roman, and Hindu. We have looked in Encarta and we need to 
confirm our findings.

Date: 09/13/97 at 18:31:53
From: Doctor Mike
Subject: Re: Ancient math symbols

Hello Carly,   

You are wise to ask for confirmation. One reputable source that I 
checked had an error in the Sumerian (Babylonian) 900. They changed 
the incorrect example in a later edition, and it still was wrong! 
So, it's best to understand things yourself, to be sure. 
   
I have not seen Encarta but some friends of mine like it. If my 
answers differ from what you found there, it does not necessarily   
mean that they are wrong or I am wrong. History is a "long time";
there have been several versions and writing styles. Even modern
numerals are written somewhat differently in Europe than in the U.S.
  
ROMAN numerals for 1, 10, 100, and 1000 are I, X, C, and M. 
  
ARABIC and HINDU are very similar to modern numerals except that a
dot may be used for the place-holder zero, ie, "1..." for 1000.  
There's another older Arabic system that's significantly different.  
   
GREEK has an older system, and a newer one (still over 2000 years 
old!) The newer system uses Greek letters for 1 to 9, 10 to 90, and 
100 to 900.  1 is written as A (alpha), 10 as I (iota), and 100 as P 
(rho). They did use a limited place system, so 111 was written as PIA.  
For 1000 and above they used a mark such as "," or "/" before the 
number of thousands.  So, 1000 is ,A or /A , and ten thousand is 
,I or /I. 
  
Now, for something completely different, SUMERIAN (Babylonian), which
is sometimes called cuneiform writing.  They used a symbol sort of 
like a "Y" for one, and a symbol sort of like "<" for ten.  There have 
been several ways of writing these, and I won't get into those 
differences. These 2 symbols were combined in pretty obvious ways, 
such as: 
    
         <YYY            and            <<<
          YYY                            <  
  
for 16 and 40. The left arrangement has one 10-symbol and six 
1-symbols for a total of 16, and the right arrangement has four 
10-symbols for a total of 40. So far you can see that these numbers 
take up a lot of space, but otherwise this system SEEMS fairly 
predictable. But hold on to your hat; it's going to be a bumpy ride 
from here on!   
      
Instead of using powers of 10 as we do for place values, they used 
powers of 60. This is similar to the way we count seconds and minutes
of time. We count 14 min. 58 sec., 14 min. 59 sec., 15 min., 15 min.
1 sec., etc. Also we count minutes up to 59 minutes and then add on
another hour. They did this for all their numbers for counting just 
anything. You asked about 100, which equals 60 + 40. I wrote it this
way because for cuneiform numerals, we put 1 in the 60's place and 
40 in the 1's or units place. We have seen 40 above, so 100 is: 
      
         Y <<<   
            <     
    
To figure out 1000 we first need to re-write it as 60*16 + 40, which
you should verify yourself. So, 16 in the 60's place and 40 in the
units place makes 1000 comes out as: 
   
         <YYY <<<
          YYY  <  
   
If that seems strange, keep in mind that it is not much stranger than
saying "16 minutes 40 seconds" instead of "1000 seconds".  
        
At this point, I'm wondering how close Dr. Math is to Encarta. (grin)
For learning some more about this I would suggest looking in a major 
encyclopedia for an article on "Number," "Numeration," or "History of
Math."  Also look in your public library catalog for books whose 
title is "Number ...." or includes the word "number."   Have fun.    
   
Good question. I enjoyed explaining it, and not just giving you the
"bottom line" answers.  I hope this helps.    
    
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/