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Subject: "Roman Numerals"     Previous Topic | Next Topic
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junglemummy
Member since Nov-7-05
Jan-04-06, 08:06 AM (EST)
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"Roman Numerals"
 
   This question will probably seem ignorant compared with some of the others on the forum, but it is something that has puzzled me since I was eight (don't wanna reveal my exact age now, but let's just say i'll never see 30 again). No-one (including maths teachers) has ever been able to give me an answer, and now my 13 year old son has asked me the exact same thing.

How did the ancient Romans do multiplication and division, eg, if they wanted to multiply 6*4, or VI*IV. People think I'm silly for not "realising" that you should convert it to our numerals, do the multiplication and then convert it back. ie, 24 becomes XXIV. But what did the Romans, who had obviously never seen our numerals, do? They must have been able to do multiplication and division with great accuracy to construct some of the things they did.

Could some kind person please explain it to me?


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  Subject     Author     Message Date     ID  
Roman Numerals junglemummy Jan-04-06 TOP
  RE: Roman Numerals alexb Jan-05-06 1
     RE: Roman Numerals alexb Jan-05-06 3
  RE: Roman Numerals M J Watkins Jan-05-06 2
     RE: Roman Numerals Alison Jan-23-06 4
         RE: Roman Numerals alexb Jan-23-06 5
             RE: Roman Numerals junglemummy Jan-23-06 6
  RE: Roman Numerals DFB Jan-23-06 7
  RE: Roman Numerals sks23cu Jul-20-06 8
     RE: Roman Numerals sks23cu Jul-09-08 9

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alexb
Charter Member
2243 posts
Jan-05-06, 01:02 AM (EST)
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1. "RE: Roman Numerals"
In response to message #0
 
   >How did the ancient Romans do multiplication and division,
>eg, if they wanted to multiply 6*4, or VI*IV.


  1. They had some form of abaci.
  2. They used tables prepared by smart people over generations.
  3. They used fingers.
  4. They used some geometric constructions.

>People think
>I'm silly for not "realising" that you should convert it to
>our numerals, do the multiplication and then convert it
>back. ie, 24 becomes XXIV.

No. The Romans were unaware of such a possibility. But the same can be said of the ancient Greek and the Hebrews who used their alphabets to name numbers. An analogue would be to use

a = 1
b = 2
...
j = 10
k = 20
l = 30
...

>They must have
>been able to do multiplication and division with great
>accuracy to construct some of the things they did.

Not necessarily. They knew to handle fractions in base 12. But I do not believe one needed that much to build the Coliseum. We shall probably never know how many buildings crashed and how many ceilings caved in because of poor design or imperfect calculations. What has survived may bear witness to their innumeracy: what has survived has been probably built many times stronger and with an exceptionally large safety margin than was really necessary.
>

Not only they did not know to count as well as your average child can do nowadays, they lived in primitive times altogether. They actually stank due to the lack of the simplest of commodities we take for granted. You probably would not want to sit next to a Ceasar in a movie theater.


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alexb
Charter Member
2243 posts
Jan-05-06, 11:40 AM (EST)
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3. "RE: Roman Numerals"
In response to message #1
 
   Some information can be found in

From Five Fingers To Infinity by F. J. Swetz.

P. 200 mentions from De Architectura by Vetruvius (ca 20 BC): Geometry, also, is of much assitance in architecture, and in particular it teaches us the use of rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level and the plummet.

PP. 221-223 describe the use by the Romans of abaci and the counting board. As Herodotus (ca 485 BC) wrote, "In writing and in reckoning with pebbles, the Greeks move the hand from left to right, but the Egyptians from right to left." (The emphasis is mine - AB.)


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M J Watkins
guest
Jan-05-06, 10:24 AM (EST)
 
2. "RE: Roman Numerals"
In response to message #0
 
   The simplest means to calculate using Roman numerals is a reckoning board.
It is defined with horizontal ines, and the lines with the spaces between them, enable the calculations. Lines are always worth five times the space beneath, and half the value of the space above. You can never have more than four in a space and 1 on a line.
The space below the lowest line is valued at one, or I; the line above is therefore worth 5 or V. The line above that is therefore 10, or X, and the next space must be - you've got it - 50 or L.
To add the numbers you just create a visual image of the original numbers with counters (the Roman word is calculi).
Thus 6 (VI) and 7 (VII) would be represented by two counters on the V line and three couners on the I space. But of course, two counters are not allowed on a line, so they convert ot be one in the space above, to give the total XIII - or 13.
To multiply you do exactly the same, but use mental arithmetic to break down the numbers, or recreate them with loads of counters.
In the example above of VI times VII you would multiply the VII by I (with the result one on the V line and 2 in the I space to show VII) and then do the same with the V - either reproducing the VII picture five times, or mentally calculating 5 times 7 to create XXXV.
Then add the XXXV and VII as in addition (the two Vs becoming one X) and you arrive at the answer - XXXXII (IV, IX, XL, etc do not work).
Division is simply a reversal of the process.
It is easiest to understand if you draw the reckoning board and use coins or games counters as the reckoning counters, and try it.


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Alison
guest
Jan-23-06, 06:16 AM (EST)
 
4. "RE: Roman Numerals"
In response to message #2
 
   I am "junglemummy" who posted the original enquiry. Every time I try to log in I get a "database error", so I am replying as a "guest". This is why I didn't get back to you more promptly.

Thank you to the people who replied. My mind has been put to rest, and I have been able to pass these explanations on to my son.

However, I must take issue with the comment about the Romans' hygiene. They were famous for building baths all over Britain including the aptly named city of Bath.

Now I just need to know what to do about the "database error" .....


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alexb
Charter Member
2243 posts
Jan-23-06, 06:23 AM (EST)
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5. "RE: Roman Numerals"
In response to message #4
 
   >Now I just need to know what to do about the "database
>error" .....

The place you post your messages is called the CTK Exchange. WHen you go there, you see in a box in the middle of the screeb icons with accompanying text: Login, FAQ, Search, etc. Press the Login and you'll see login/password input conrols.

The ones that appear in the upper left corner of the pages at the site have a different function. You should not worry about that.


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junglemummy
Member since Nov-7-05
Jan-23-06, 08:38 AM (EST)
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6. "RE: Roman Numerals"
In response to message #5
 
   Thanks, Alex, for

(a) telling me how to log in again - I was using the left hand corner
(b) your reply to my original post.


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DFB
guest
Jan-23-06, 03:01 PM (EST)
 
7. "RE: Roman Numerals"
In response to message #0
 
   These sit's are helpful. Check them out.
https://www.phy6.org/outreach/edu/roman.htm
OR
https://en.wikipedia.org/wiki/Roman_arithmetic


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sks23cu
guest
Jul-20-06, 03:18 PM (EST)
 
8. "RE: Roman Numerals"
In response to message #0
 
   >How did the ancient Romans do multiplication and division

They used a counting board like the Salamis Tablet, just like the Greeks and Babylonians before them.

Roman Numerals were used only for recording the results.

Multiplication utilizes addition, and division utilizes addition of negative numbers.

See this link for further explanations and examples:

https://home.comcast.net/~sks23cu/SalamisTablet/

-sks


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sks23cu
guest
Jul-09-08, 07:54 AM (EST)
 
9. "RE: Roman Numerals"
In response to message #8
 
   >>How did the ancient Romans do multiplication and division
>
>They used a counting board like the Salamis Tablet, just
>like the Greeks and Babylonians before them.
>
>Roman Numerals were used only for recording the results.
>
>Multiplication utilizes addition, and division utilizes
>addition of negative numbers.
>
>See this link for further explanations and examples:
>
>https://home.comcast.net/~sks23cu/SalamisTablet/
>
>-sks

The link has changed to https://sks23cu.net/TSA/.

Or, do a Google search on "The Stephenson Abacus".

-sks


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