Roman Numerals: Charts, History and Numerology

How to write 2011 using Roman numerals? Is it a lucky number?

2010-12-31T13:47:15Z

Do you need to write 2011 using Roman numerals? It's easy!

2011 = MMXI

Note the fact that if you use the Roman system the numer 2011 cannot be considered "lucky" as it is sometimes believed when two parts of a given number add up to the same value, which is clearly the case if you stick to the Arabic numerals:

2+0 = 1+1

The Lost Symbol - Decoding the ISBN (0385504225). From Solomon Key to Jupiter Square!

2009-09-14T15:36:42Z

It occurred to me that for the first time in his career as a novelist Dan Brown was in the position to be extremely capricious, even to the most ridiculous degree. Remember, Da Vinci Code was his first success, quite unexpectedly. Deception Point and Angels and Demons only became widely known after Dan Brown became famous for his third novel. Now, why not use this opportunity to pick an ISBN that would carry some symbolic meaning? Wouldn't that be a nice touch to what Dan Brown's publisher hopes to be a highly successful book?

One must keep in mind that ISBN numbers cannot be chosen randomly. Every publisher is assigned blocks of ISBNs, all of them usually contain similar sequences. So, Dan Brown would have to get quite creative. Still, it did not take long for me to discover one very striking fact. If you add up the digits in the ISBN of "The Lost Symbol" you get the number 34:

0+3+8+5+5+0+4+2+2+5=34

Anyone familiar with numerology will immediately notice that the universally accepted lucky number 7 can be based on 34: 3 + 4 = 7. Also, according to some, 34 "signifies realization of the man." You can easily find more random minutiae connected with this number (e.g. in Dante's Commedia there are 34 cantos dedicated to Hell, while Purgatory and Paradise each get 33 cantos). But here is the most interesting fact. The numbers 1 through 16 can be arranged in the so called Jupiter's Table, a magic square where every line of numbers has the sum of 34:

16    3 2   13
5 10   11    8
9    6    7 12
4 15   14 1

There are variations in the way the numbers are oriented in the square. Of course, "serious" numerologists use Hebrew letters with their numeric values.

d

Amulets containing the Jupiter table are supposed to bring wealth, prosperity etc. As far as I can tell, there are many Masonic amulets of this sort. One was supposedly owned by Joseph Smith, the founder of Mormonism.

A word of caution, however. When you write 34 using Roman numerals you get XXXIV, which in reverse reads VIX (XX), meaning "hardly", "with difficulty", "barely." Even worse, 34/2 = 17 and 17(XVII) has been feared for quite some time because when you rearrange the letters you can get VIXI - "I have lived" (meaning "I am dead"), therefore the number 17 is often superstitiously avoided. What will happen with Dan Brown and his writing career? Time will tell, but let's hope that Dan Brown will not find himself singing Charley Patton's highly numerological "34 Blues":

"I ain't gonna tell nobody,
'34 have done for me
I ain't gonna tell nobody what
'34 have done for me
Took my roller, I was broke as I could be."

UPDATE

Because I made this discovery when the book was not available yet I had no idea that Dan Brown uses this exact Jupiter Square as a clue in his book! All of a sudden, the number 34 encoded in the ISBN does not look so coincidental... Here is a fragment of Albrecht Dürer's Melencolia I described in the novel:

I will add something else here... Some folks are saying that the complete ISBN includes 978. It looks like this is simply a translation of the number into a different ISBN standard (ISBN-10 to ISBN-13). In fact, it is difficult to find a book that does not have 978 as the first digits of ISBN-13, thus rendering this part of the ISBN unchangeable.

What number system did the Romans use in complex calculations?

2009-03-18T22:13:01Z

One look at any mathematical formula in Roman numerals is enough to realize that to use this system for anything complex would be extremely difficult, if not impossible. It takes forever to simply right down most numbers! The truth is, the Romans were not overly patriotic when it came to number systems. All the feats of engineering, temples, arenas and palaces would have never become a reality were it not for the ample use of Greek numerals! Roman engineers and scientists were usually either Greeks or Greek-educated Romans (sometimes completely bilingual). The Greek system was much more versatile, compact and well suited for any calculations known to Ancient mathematicians.

Superbowl numbers - Roman numerals

2009-01-31T20:25:06Z

And for all of you sports fans out there, Superbowl numbers in Roman numerals, truly one of the major sources of interest towards the ancient numeric system. Of course, the very first Superbowl did not have a number at first, but the rest of the sure did. I believe every Superbowl also had an official logo.

1 = I

2 = II

3 = III

4 = IV

5 = V

6 = VI

7 = VII

8 = VIII

9 = IX

10 = X

11 = XI

12 = XII

13 = XIII

14 = XIV

15 = XV

16 = XVI

17 = XVII

18 = XVIII

19 = XIX

20 = XX

21 = XXI

22 = XXII

23 = XXIII

24 = XXIV

25 = XXV

26 = XXVI

27 = XXVII

28 = XXVIII

29 = XXIX

30 = XXX

31 = XXXI

32 = XXXII

33 = XXXIII

34 = XXXIV

35 = XXXV

36 = XXXVI

37 = XXXVII

38 = XXXVIII

39 = XXXIX

40 = XL

41 = XLI

42 = XLII

43 = XLIII

What made Roman numerals easy to use?

2009-01-15T01:42:18Z

When modern students are faced with having to learn the Roman system they often wonder how on earth anyone ever found this number notation convenient for any sort of calculations. The answer is actually rather simple. Yes, Roman numerals are not great for complicated calculations. However, they were extremely convenient when they were used at the time of their origin. Imagine having to carve Arabic numerals on wood or bark. Now imagine achieving the same objective using Roman numerals. The difference is striking. All the letters used in the Roman system can be carved with a few simple cuts: I, V, X, L, < (for C), |> (for D), M. There is evidence that a similar system was still used in the 19th century, in some rural communities in Italy, by shepherds who needed to keep track of their flocks. By the way, the simplicity of these symbols may indicate that they are not related to the Latin alphabet, but are rather independent of it, except perhaps C and M, which are probably dependent on the Latin words centum (one hundred) and mille (one thousand).

Roman numerals in sports: the infamous UF t-shirt

2009-01-06T21:45:00Z

Come Superbowl time, every football fan in the US is subject to a mandatory annual rediscovery of Roman numerals. Of course, the proper way of referring to Superbowl match-ups requires the use of this antiquated, yet beautiful system. Apparently, this yearly refresh course is not enough for some people. This t-shirt that was made by the University of Florida in 2006 should serve as a somber reminder of the sad state of affairs in our education when it comes to Roman numerals. Instead of MMVI (2006) these shirts were printed as shown, proudly displaying XXVI (26). To all math teachers out there, use this in class to prove to your students that not knowing how to use Roman numerals can can you fired!

Roman Numerals 1-25 ( I-XXV ) - a video

2008-12-19T03:38:48Z

Roman Numerals 1-25 are displayed in this video. Complete with the audio.

Roman numerals: a field guide

2008-12-19T00:13:36Z

The ultimate Roman numerals chart! This guide is an essential reference for everybody who has to deal with Roman numerals. Includes a Roman numerals chart (1-5000) and a look-up table of alphabetically arranged Roman numerals, with some variants and erroneous renditions.

Roman Numerals: a field guide

Roman Numeral 9 (and 4)

2008-12-17T01:54:57Z

It is usually assumed that the correct way of expressing number 9 in Roman numerals is IX. This assumption is generally correct, but very often you will see number 9 shown as VIIII. Although this looks quite strange and almost wrong to the modern eye, this was a completely valid way of writing 9 in Roman times. My theory is that using VIIII instead of IX creates a sense of a natural progression of numbers. If you decide to use this old convention for your own numbering purposes, make sure that instead of IV you use IIII for 4, otherwise the resulting numbers may look inconsistent.

Puzzles with Roman numerals

2008-11-19T02:08:48Z

This passage is taken from Number Stories of Long Ago, by David Eugene Smith:

Titus liked to puzzle a chum of his named Caius, and one day he asked him this question : " What is the number that becomes one more when one is taken away from it ?"

"Your head," replied Caius, "must be just plain wood."

But when Titus wrote IX on the stone pavement and said to Caius, "Now take away the I and tell me what you have left,"Caius saw that the wooden head had something in it after all.

Then Caius, remarking that he could think of many other numbers that would answer just as well, asked this question: "What is the number that becomes ten more when ten is taken away ? "Titus then asked Caius if he knew that half of nine was four, and Caius replied that he must be dreaming. But Titus pointed again to IX and asked Caius to take the upper half of it and see if it was not IV. Then Caius said that he could show that half of twelve was seven.

"That is nothing," said Titus; "half of thirteen is eight."

"That is easy," said Caius ; "but can you take one hundred from four hundred and
have five hundred left ?"

Roman numerals: Present day uses

2008-11-16T10:58:45Z

I decided to enumerate (pun absolutely intended) all the uses of Roman numerals today. Granted, this will not be a complete list at first. I may never even get to the bottom of the issue, but this should be useful anyway...

Clocks
Sundials
Introductions, section numbers, volume numbers etc. in modern books
After the names of monarchs, popes and royally conceited individuals
Centuries
Dates on buildings
Dates in copyright information (movies, especially)

Home-made sundial clock with Roman numerals

2008-10-30T21:48:58Z

Sundials are typically associated with Classical Antiquity and for a good reason. They were widely used in Ancient Greece and Rome. The simplicity of their construction made them a lot more affordable than, for instance, clepsidras. As a result, Roman numerals are still traditionally used on sundials. This particular one uses IV for 4, and not IIII as is often seen on mechanical clocks. I actually have encountered a book claiming that Ancient Romans never used IIII instead of IV, but clockmakers have somehow adopted this erroneous representation of number 4. Well, that is simply not true. At this time I am not going to provide any epigrapic evidence, but let me just mention that IV would have also been used as an abreviation for IVPITER, Jupiter. To avoid confusion it was quite reasonable to use IIII. I also believe that on a clock with 12 numbers IIII (And VIIII for 9, incidently) provides a better sense of progression of time (see Ucello's clock), because time is all about forward progress, while the more accepted variations of these numerals imply looking back and subtracting the first part of the compound numeral from the higher value of the second part. Well, you know what I mean. The sundial clock, however, is not capable of showing 12 hour time. It is possible that using classic forms for IIII and IV helps create a more balanced look. Anyway, here is how to make a sundial clock, as described by Archibald Williams in Things Worth Making. Just remember that the present daylight savings time system has to be accounted for. Also, I would suggest picking a sundial motto, as it is quite customary in the business of sundial making.

A HOME-MADE SUNDIAL

A sundial is an interesting thing to have on a garden wall or the stump of a tree, or to set in a south-facing window. Ordinary flat and vertical sundials require the use of advanced mathematics; but that to be described is within the capacity of any handy person.

One begins by making a cross of thin metal. Brass, copper, zinc are all suitable; copper is the best. The cross may either be cut in one piece out of the sheet, or be compounded of a vertical piece and a cross piece riveted together at the point of crossing. The dimensions given in Fig. 44, a, are for a small dial, but they may be modified to suit individual fancy, provided that the circumferential length of the cross-piece B be the same as the distance between the centres of the holes in A. Mark off the cross-piece into twelve equal parts, and subdivide each of these into quarters or twelfths. The lines may be scratched or etched with acid. For the hours use the Roman numerals, which, being made up of straight lines, are very easily engraved.

When this has been done, bend both pieces to a truly semicircular shape. To get the curve correct one must cut out a cardboard circle with half its circumference equal to the length of the crosspiece piece and use it as a template. The exact diameter can best be arrived at experimentally. If copper or brass be used, anneal it by red-heating and plunging into cold water before it is bent.

As the pieces are easily distorted, if of thin metal, it is advisable to solder to the back of each a rib of the same metal, cut out with the aid of the template already made. One rib will have to be severed at the crossing-point to give room to the other rib, to which it should be soldered. If stout strip metal be used, this backing will be unnecessary, but in this case a wooden template had better be cut to the right curve to enable the shaping to be done accurately by hammering. After shaping, slip a piece of quite straight copper wire through the holes in A, and make them fast with solder.

The dial is now fixed facing the south (in our northern latitudes), with the wire sloping towards the north, and making with the horizontal an angle approximately equal to the latitude of the place --for London, about 51 1/2 degrees. To state the matter otherwise, the axis of the wire should point to the Pole Star. The orientation must be established accurately by a compass.

The dial is most easily fixed by means of a little wooden saddle crossing A, with a screw at each end penetrating either a horizontal base board (as shown) or the face of a wall -- in which case the saddle would occupy the position indicated by the dotted lines.

When consulting the dial at any time, add or subtract the noon difference for the day from the shadow reading to arrive at clock time. At most the noon difference is only about a quarter of an hour.

Paolo Ucello's clock with Roman numerals

2008-10-25T06:33:37Z

This clock face, painted by Paolo Ucello in 1443 for the Duomo in Florence is rather unusual in that the numbers are depicted counter-clockwise. The style of the numerals is also interesting (look at the shape of the X). It also appears that the way Ucello chose to write some of the numbers is much more fitting for a clock. In fact, I would recommend to use IIII instead of IV and VIIII instead of IX. This style of numbers requires less space and their progression looks more natural.

An old experiment with Roman numerals

2008-10-25T04:42:22Z

Robert Yerkes of Harvard reported the following experiment in Science XX, No 505

I have chosen ten well-educated, and in most cases scientifically trained individuals, and determined for each the time necessary for the writing of the Roman and the Arabic numerals from 1 to 100 and the number of errors made, also the time necessary for the reading of the Roman and the Arabic numerals from 1 to 100 when they were irregularly arranged so that the reader did not know what order to expect. In all cases the number of errors made unconsciously was recorded. These measurements furnish the following startling averages: It takes three and one third times as long to write the Roman numerals from 1 to 100 as the Arabic, and the chance of error is twenty-one times as great; it takes three times as long to read the Roman numerals from 1 to 11O as the Arabic, and the chance of error is eight times as great.

In case of a quick and accurate mathematician, whose familiarity with the Roman system
surpassed that of most of the individuals tested, the results were: time for writing
Arabics, 107, errors, 0; time for writing Romans, 357, errors, 5; time for reading Arabics, 62, errors, 2; time for reading Romans, 131, errors, 5. For one well-trained scientist, who has cause to use the Roman system almost every day, the number of errors in the rapid reading of the Romans was 151 These figures certainly indicate the desirability of using the Arabic system wherever there is no urgent need for the simultaneous use of two or more systems of numerals. Even if there were no saving of time and strain by the avoidance of the cumbersome Roman symbols, the far greater accuracy gained by the use of the Arabic system should at once settle the matter for all scientists.

Interesting results. I would like to note two things, however. The Roman system is slightly more aesthetically pleasing and even more appropriate in certain cases. In books, it allows to have separate pagination for the introductory part etc. Also, from the point of view of the information theory, the system that intrinsically involves using more symbols should be more redundant and less prone to transmission errors. I think that, above all, this experiment proves the need to learn Roman numerals and to develop better control over them.

Roman numerals chart

2008-10-24T18:46:17Z

I=1 V=5 X=10 L=50 C=100 D=500 M=1000



I	1	XXXII	32	LXIII	63	XCIV	94
II	2	XXXIII	33	LXIV	64	XCV	95
III	3	XXXIV	34	LXV	65	XCVI	96
IV	4	XXXV	35	LXVI	66	XCVII	97
V	5	XXXVI	36	LXVII	67	XCVIII	98
VI	6	XXXVII	37	LXVIII	68	XCIX	99
VII	7	XXXVIII	38	LXIX	69	C	100
VIII	8	XXXIX	39	LXX	70
IX	9	XL	40	LXXI	71	EX.
X	10	XLI	41	LXXII	72	DI	501
XI	11	XLII	42	LXXIII	73	DL	550
XII	12	XLIII	43	LXXIV	74	DXXX	530
XIII	13	XLIV	44	LXXV	75	DCCVII	707
XIV	14	XLV	45	LXXVI	76	DCCCXC	890
XV	15	XLVI	46	LXXVII	77	MD	1500
XVI	16	XLVII	47	LXXVIII	78	MDCCC	1800
XVII	17	XLVIII	48	LXXIX	79	CM	900
XVIII	18	XLIX	49	LXXX	80
XIX	19	L	50	LXXXI	81
XX	20	LI	51	LXXXII	82
XXI	21	LII	52	LXXXIII	83
XXII	22	LIII	53	LXXXIV	84
XXIII	23	LIV	54	LXXXV	85
XXIV	24	LV	55	LXXXVI	86
XXV	25	LVI	56	LXXXVII	87
XXVI	26	LVII	57	LXXXVIII	88
XXVII	27	LVIII	58	LXXXIX	89
XXVIII	28	LIX	59	XC	90
XXIX	29	LX	60	XCI	91
XXX	30	LXI	61	XCII	92
XXXI	31	LXII	62	XCIII	93