Roman Numerals & Fractions.

[Gaius Octavius]

This site makes it a little more clear:

 

http://www.paullewis.co.uk/

 

Click on 'Roman Numerals'.

Edited March 3, 2007 by Gaius Octavius

[Ruthe]

This site makes it a little more clear:

 

http://www.paullewis.co.uk/

 

Click on 'Roman Numerals'.

 

I am sorry to say that the reference given has one or two points with which I cannot agree. After clicking on the link 'Roman Numerals' you are presented with a page with several more links. There is a group of links that starts with 'How Roman Numerals Work'. Click this link to a yet another page. This has a very complete description of Roman numerals and how they were written including explanation of the rules for forming any required value.

 

When you reach the section subtitled 'Fraction', the author makes a number of incorrect or incomplete statements. First, the table of fractions is far from complete and only shows one form of symbols for the truncated list of fractions, missing out any fractions less than 1/12, and alternative symbols for the ones he does list. He then states that "Other fractions could not be depicted in Roman numerals" which is clearly false since many other fractions existed and had specific names and symbols. Furthermore, Romans often indicated other fractional values for which they did not have a specific name or symbol by combing two or more of their duodecimally based fractions to provide a very close approximation to the required fraction.

 

Secondly, in the subsection titled "Zero", the author correctly identifies that the Romans had no symbol for zero, but certainly had the concept in the use of an empty column in their abacus, but then implies they had no concept of a "place" value system when it is obvious that their decimally based bi-quinary abacus was the concrete embodiment of that very idea. What is accepted is that this knowledge was not transcribed to the Roman written format for numeric values but was easily transcribed directly from abacus to the Roman written format. In column one, beads in the bottom slot represented the same number of "I"s while the bead in the top slot in the counted position was a "V". For the second column these were "X"s and an "L" respectively, and so on for succesive columns giving "C"s and a "D", "M"s or a "(I)" and a "(X)" and so on.

 

I recommend the majority of this information but with the provisos I have noted above.

[Gaius Octavius]

Ruthe, you ought to e-mail the guy.

[SKStephenson]

That web page shows an "incorrect" use of subtractive notation, i.e. IIX (or was it XXC?). But the rules were put in place, I believe, after the Romans, in Medieval times.

 

Subtractive notation is actually used to represent counters on a counting board style abacus, e.g.:

 

IIXXooI = 18 5/6

(-).....(+)

-----|o---o X

.....|..... V

---oo|----o I

.....|..... S

---oo|----- o

 

[i would like NOT to use the periods, but don't know how to keep spaces from being deleted.]

 

Preferred representations on an abacus:

IIV, IV, IIX, IX, etc.

 

This conserves space by dramatically reducing the total number of counters and by reducing the number of counters on a line or space.

 

More explanations here: http://www.ieeeghn.org/wiki/index.php/Ancient_Computers

Edited August 11, 2010 by SKStephenson