Roman Numerals

Nowadays the modern conversion of 444 into Roman numerals is now considered to be CDXLIV which doesn't lend itself quite easily to mathematical calculations but there exist historical evidence to suggest that the ancient Romans would have calculated the equivalent of 444 on an abacus calculating frame as CCCCXXXXIIII and then logically abridged it to IVLD thus facilitating the required calculations as follows:-

MDCCLXXVI+CCCCXXXXIIII = MMCCXX => 1776+444 = 2220

MDCCLXXVI+IVLD + MMCCXX => 1776+(500-56) = 2220

MDCCCLXXVI-CCCCXXXXIIII = MCCCXXXII => 1776-444 = 1332

MDCCLXXVI-IVLD = MCCCXXXII => 1776-(500-56) = 1332

Note that in mathematics 1776-(500-56) becomes 1776-500+56 = 1332 and that negative and positive numerals once went in opposite directions somewhat similar to today's number line.

QED

The ancient Romans probably worked them out as follows:-

MDCCLXVIIS+SIX = MDCCLXXVI => 1767.5+(10-1.5) = 1776

MDCCLXVIIS+VIIIS = MDCCLXXVI => 1767.5+8.5 = 1776

Note that the rules as we know them to day now governing the Roman numeral system had nothing to do with the ancient Romans because they were introduced during the Middle Ages.

QED

Today we would convert 1444 into Roman numerals as MCDXLIV which is a non-starter in terms of integration with other numerals.

But in ancient Rome the Romans would have calculated the equivalent of 1444 as MCCCCXXXXIIII which can be logically transformed to IVLMD yet still retaining its original numerical value thus enabling addition to be carried with speed and ease as follows:-

IVLMD+DLXVIII = MMXII (-56+1500)+(568) = (2012)

Alternatively:-

MCCCCXXXXIIII+DLXVIII= MMXII (1444)+(568) = (2012)

So the real rules are that when in Rome do as the Romans do.

QED

Under todays rules governing the Roman numeral system (which incidentally had nothing to do with the Romans because these rules were introduced during the Middle Ages) we would convert 1492, 14 and 49 into Roman numerals, in direct comparison with the Hindu-Arabic numeral system, as MCDXCII, XIV and XLIX respectively which makes mathematical interaction amongst them quite cumbersome and chaotic.

But when in Rome do as the Romans do because there is evidence to suggest that the ancient Romans would have calculated the equivalent of these numbers using either of the following formats:-

XMDII+IXV = MDVI => (1502-10)+(15-1) = (1506)

MDVI+IL = MDLV => (1506)+(50-1) = (1555)

Alternatively:-

MCCCCLXXXXII+XIIII = MDVI => (1492)+(14) = (1506)

MDVI+XXXXVIIII = MDLV => (1506)+(49) = (1555)

Note that: 5*I=V, 2*V=X, 5*X=L, 2*L=C, 5*C=D and 2*D=M

Roman numerals: M=1000, D=500, C=100, L=50, X=10, V=5 and I=1

QED

The rules as we now know them today governing the Roman numeral system have absolutely nothing to do with the ancient Romans whatsoever because they were changed in the Middle Ages presumably to make the Roman numeral system more compatible with the Hindu-Arabic numeral system that was gradually being introduced into Western Europe via Spain at the time and as a result the Hindu-Arabic numerals of 159 and 149 are now considered to be CLIX and CXLIX when converted into Roman numerals respectively which does not quite lend themselves easily towards mathematical interactivity between each other or any other numerals for that matter but nowadays we can extrapolate from reliable historical sources that the ancient Romans would have probably calculated the given integers as in any of the following formats:-

CLVIIII+CXXXXVIIII = CCCVIII => 159+149 = 308

ICLX+ICL = CCCVIII => (-1+160)+(-1+150) = 308

CLVIIII+CXXXXVIIII = X => 159-149 = 10

ICLX-ICL = X => (-1+160)-(-1+150) = 10

Note that the above calculations are pretty fundamental and were fairly easy to work out but for more complicated calculations the ancient Romans would have made usage of an abacus calculating device.

Nowadays 9-19-1999 is officially notated as IX-XIX-MCMXCIX in Roman numerals.

But there exist historical evidence to show that the ancient Romans would have worked out the equivalent of 9-19-1999 on an abacus counting device as follows:-

VIIII-XVIIII-MDCCCCLXXXXVIIII => 9-19-1999

And then abridged them logically in written format as follows:-

IX-IXX-IMM => (10-1)-(20-1)-(2000-1)

QED

This question has already been answered by myself but someone else has entirely deleted the original answer probably for plagiarizing purposes so here we go again:-

It is written that at one time in the distant past the Hindu-Arabic numerals or digits of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 were once encoded with secret geometrical symbols inasmuch that the first digit of 1 had either an arc or an angle of 36 degrees hidden in it and then thereafter each consecutive digit was increased by increments of 36 degrees by means of arcs and angles or a combination of both in which the digit 0 finally consisted of 360 degrees.

As a consequence of these concealed codes the digit degree sum of any number from 1 to infinity would always finally total to 9 degrees as the following example shows:-

Digit degree sum of 2357 = 36*(2+3+5+7) = 612 => 6+1+2 = 9 degrees

Over the past thousands of years Hindu-Arabic numerals have been transformed into the configuration that we use today but the zero figure at one time probably resembled a circle which even today consist of ten 36 degree arcs amounting to 360 degrees.

QED