I suppose it is fitting to make this entry on the day that Italy won the world cup (though I was cheering for France). I was on Columbia’s campus yesterday and noticed the ubiquitous roman numeral date of erection on the buildings. Figured it was time to really learn this archaic system once and for all. With a little study I was able to do a variety of numbers with ease, and discovered that I had recently made an error writing the number 40 as XXXX, d’oh !

Here are the letters that you need to know:
I = 1 (no surprise)
V = 5
X = 10
L = 50 (news to me)
C = 100 (apparently this is because there were 100 men in a group of centurions)
D = 500
M = 1000

Many of us are familiar with most of these, and it is no surprise that you combine the
letters together to count up: I, II, III, IV, V, VI, VII, VIII, IX, X. 1 - 10 are no problem. We are used to seeing the I in front of the V and X to indicate 4 and 9. That was about all I knew about the rules of combining the letters; prefix letters subtract and suffix letters do addition. Turns out this isn’t enough. For example IL does not equal 49 even though 1 - 50 makes logical sense. Here are the rules of combination I found:

1. You may put one and only one smaller value letter before a larger number: IV, IX, CD, CM, but not IIX or CCM
2. You may put up to three equal or smaller value letters after a number: VIII, CX, MMM, MDC, but not XXXX or VIIII
3. This next one is a little difficult to explain cleanly, so I’ll try with examples. 99 = XCIX = ((10 - 100) + (1 - 10)), not IC, 45 = XLV = (10 - 50 + 5) not VL. I’m sure a mathemetician could explain this cleaner, but my rule of thumb is you have to use a prefix character that is the next smallest power, so for 100 you can only decrement with 10, 1000 with 100, 10 with 1, this also goes for the ‘5′ values V, L, and D. Thus 40 is 10 - 50, 400 is 100 - 500. Illegal combinations that break this rule: XC, XD, XM, LC (makes no sense 100 - 50 is 50), LD, LM and I with anything other than X, IL, IC, ID, IM.

Now armed with these rules we can easily construct a variety of numbers. Here is the year I was born MCMLXXII = (1000 + (100-1000) + 50 + 10 + 10 + 1 + 1) = 1972.
Here are some other example to drive the point home:

• 42 = (10 - 50 + 1 + 1) = XLII
• 666 = (500 + 100 + 50 + 10 + 5 +1) = DCLXVI
• 1666 = MDCLXVI (note, this is every numeral in order from largest to smallest)
• 3745 = MMMDCCXLV (you don’t see numbers larger than the current year that often)
• and finally MMVI = 2006

Here is a great roman numeral calculator that I used to test myself: Roman Numbers

This entry was posted on Sunday, July 9th, 2006 at 9:20 pm and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.