Talk:Roman arithmetic

CPU Arithmetic

Shibboleth is apparently correct about multiplying and dividing in modern machine language (I haven't tried it much since about 1980), although I wish he had explained it a little to Mr. Hardy. The mul, div, imul, idiv, fmul and fdiv commands at x86 instruction listings are apparently intended for multiplying and dividing. Art LaPella 02:38, Sep 4, 2004 (UTC)

The CPU in modern computers generally is only able to directly perform these two simple operations. was deleted from the article.

The machine language may have the instructions, but that does not mean the CPU actually multiplied or divided as a single step. In the ALU/FPU of many CPUs, the actual multiplication is a series of shifts or additions performed by the processor. The same holds true for division. The orginal text did not state that CPUs lacked instructions to perform more than addition or subtraction (which was true with the Z80's instruction set). I wish Shibboleth had taken the time to discussed it here first, rather than just making the deletion from the article. --Denise Norris 04:31, Sep 4, 2004 (UTC)

Historical evidence

Is there any evidence that the algorithms presented here were, in fact, the ones used by ancient romans? --Mathish 01:08, 13 November 2005 (UTC)

I would also like to know if these algorithms are historical. There is an alternate method using cancellation for addition of values with subtractive notation, and multiplication can be done with a (presumably modern, albiet simple) multiplication table rather than the iterative solution presented here. --Dcorrin 16 November 2005

I found this guide to Roman Multiplication, but I don't know his sources. It seems like a much easier method of multiplying MDCCLXIII by CCXVII, and other large quantities. http://www.phy6.org/outreach/edu/roman.htm ih8evilstuff 15:52, 6 June 2006 (UTC)

If the Romans used it, surely they must have known why it works. Even if they didn't know the binary number system, they knew that a x b = a/2 x 2b, right? It's essentially still repeated addition, but just with a trick to do it faster.

While the multiplier is odd, remove one from the multiplier and add the multiplicand to the result. Use the aforementioned identity: halve the multiplier and double the multiplicand - this doesn't change the result. D.C. al fine.

You don't have to know binary to figure this out (it could be a nice stepping stone though, in either direction). Also note that 123 x 456 is a lot harder than 2 x 28044, the Romans must have known that too. Shinobu 12:40, 2 August 2006 (UTC)

Consider this:

The Romans used the abacus extensively, and Roman numerals efficiently record abacus results (hence 'IV'). The abacus is a very effective tool in experienced hands, and I very much doubt that any Romans would have bothered with rather cumbersome symbol-manipulation.

Trying to apply the symbol-manipulation approach to Roman numerals says more about expectations of people use to Arabic numerals, which are effective for such methods, than about Roman mathematics.

It all seems a bit of a red herring to me. Sawatts 17:39, 16 July 2007 (UTC)

The Story of 1 maintains that math was done with the abacus, and results were recorded in Roman numerals. Anyone know its source? — Preceding unsigned comment added by True Pagan Warrior (talk • contribs) 18:57, 19 October 2011 (UTC)

Multiplication and division?

Someone should mention this:

To multiply using Roman numerals, say XXIX × XVII (29 × 17), convert it to:

(XX + IX) × (X + VII)

Then XX × X = CC, IX × X = XC, XX × VII = CXL, IX × VII = LXIII.

To multiply by 10, increase the "rank" by one: I --> X, V --> L, X --> C, L --> D, C --> M, and so on.

Add them up: CC + XC + CXL + LXIII = CDXCIII.

If anyone can figure out how to do division, I'd be pleased to hear from you! --121.7.203.64 (talk) 03:04, 30 May 2009 (UTC)

I don't know how the Europeans did arithemtic with Roman numerals, but the direct approach is messy. For example, 29 × 17 is XXIX × XVII. We calculate this by proceeding from left to right, as:

    XXIX
  × XVII
  ------
    CCXC (X)
    LLVL (V)
    XXIX (I2)
  + XXIX (I1)
  ------

Note that each subtotal line can be performed left-to-right. This requires a multiplication table where I×I=I, I×V=V, V×V=XXV, V×X=L, X×X=C, etc. Now combine the subtotals, separating them into digit groups that preserve their left-to-right order:

CC XC LL VL XX IX XX IX

Now reorder and combine groups of the same rank, replacing terms like VV and VL with their canonical equivalents:

CC XC C XXXXV XXXX VIIII VIIII
CCC XCX XXX XXXX V VV IIII IIII
CCC C  XXXXX XX V X IIIII III
CCCC L XXX V V III
CCCC L XXX X III
CCCC LXXXX III
CD XL III
CDXLIII

So XXIX × XVII = CDXLIII, which is 29 × 17 = 443. Yep, this is ugly. — Loadmaster (talk) 21:35, 17 September 2009 (UTC)

Ancient Roman Numeral System

The Roman Numeral System was used extensively on coins. It was a simple additive system and the symbols IV, IX, IL, IC, ID and IM were not part of it. Simply put it was I,II,III, IIII,V,VI, VII,VIII,VIIII,X then the I through VIIII was repeated through the next four Xs until the L symbol was used at XXXXVIIII. Clear and convincing evidence of the accuracy of my explanation comes from Roman Numerals on coins up to the 18th century when the use of combined symbols IV and IX came into vogue to show a single digit symbol 4 or 9. The Holy Roman Empire that lasted from roughly 650 A.D. to 1850 A.D. used these symbols correctly on their state and ecclisiastical coins and the Vatican and Papal states in Italy used them corectly too. Most of this crap has been promoted under the banner of artistic license. As time passes it gets worse as now math symbols are being interceded between the symbols too.

By the end of the Summer I plan to release essays on the original RN System, RN System Uses, RN Systems and Modern Calendar Systems, RN Symbols Used In Error. The Impact of Using Roman Numerals (that are not part of the orignal) In Modern Practice.

If you have evidence of actual use of Roman Numerals Before 1500 when Arabic Numerals became popular in Europe I would be very interested. The adoption on Gregorian Calendar and Arabic Numerals occurred in Great Britian in MDCCLII and it's Colonies including the U. S. A.

Glen Shake —Preceding unsigned comment added by 72.181.213.4 (talk) 21:36, 13 June 2009 (UTC)

Just unfounded conjecture

I believe and the discussion at Wikipedia_talk:WikiProject_Mathematics#Roman_arithmetic seems to confirm that the Romans never did arithmetic in a way proposed by this article. It is a modern day fancy and not even a notable one as shown by the lack of citations. Therefore I have prodded it. Dmcq (talk) 02:20, 21 October 2011 (UTC)

Your argument that because Roman's used a counting table or abacus so therefore they did not do manual arithmetic is unconvincing as saying that because the modern-era had slide rules and IC-chip calculators the modern era did not do arithmetic manually. It is already noted that the article needs attention from an expert and clearly the citation list could be longer. I believe the article can be improved and should not be deleted.--D. Norris 05:28, 21 October 2011 (UTC)