Roman Numerals
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Roman Numerals

Roman numerals, the numeric system in ancient Rome, use combinations of letters from the Latin alphabet to signify values.

Roman numerals have no concept of the number zero, nor do they have a rigid concept of place-value. Because of this, the character length of numerals increases and decreases raggedly as numbers increase.

Below are the numbers 1-500 displayed in Roman Numerals. You can read more about the format of the numbers here

1I
2II
3III
4IV
5V
6VI
7VII
8VIII
9IX
10X
11XI
12XII
13XIII
14XIV
15XV
16XVI
17XVII
18XVIII
19XIX
20XX
21XXI
22XXII
23XXIII
24XXIV
25XXV
26XXVI
27XXVII
28XXVIII
29XXIX
30XXX
31XXXI
32XXXII
33XXXIII
34XXXIV
35XXXV
36XXXVI
37XXXVII
38XXXVIII
39XXXIX
40XL
41XLI
42XLII
43XLIII
44XLIV
45XLV
46XLVI
47XLVII
48XLVIII
49XLIX
50L
51LI
52LII
53LIII
54LIV
55LV
56LVI
57LVII
58LVIII
59LIX
60LX
61LXI
62LXII
63LXIII
64LXIV
65LXV
66LXVI
67LXVII
68LXVIII
69LXIX
70LXX
71LXXI
72LXXII
73LXXIII
74LXXIV
75LXXV
76LXXVI
77LXXVII
78LXXVIII
79LXXIX
80LXXX
81LXXXI
82LXXXII
83LXXXIII
84LXXXIV
85LXXXV
86LXXXVI
87LXXXVII
88LXXXVIII
89LXXXIX
90XC
91XCI
92XCII
93XCIII
94XCIV
95XCV
96XCVI
97XCVII
98XCVIII
99XCIX
100C
101CI
102CII
103CIII
104CIV
105CV
106CVI
107CVII
108CVIII
109CIX
110CX
111CXI
112CXII
113CXIII
114CXIV
115CXV
116CXVI
117CXVII
118CXVIII
119CXIX
120CXX
121CXXI
122CXXII
123CXXIII
124CXXIV
125CXXV
126CXXVI
127CXXVII
128CXXVIII
129CXXIX
130CXXX
131CXXXI
132CXXXII
133CXXXIII
134CXXXIV
135CXXXV
136CXXXVI
137CXXXVII
138CXXXVIII
139CXXXIX
140CXL
141CXLI
142CXLII
143CXLIII
144CXLIV
145CXLV
146CXLVI
147CXLVII
148CXLVIII
149CXLIX
150CL
151CLI
152CLII
153CLIII
154CLIV
155CLV
156CLVI
157CLVII
158CLVIII
159CLIX
160CLX
161CLXI
162CLXII
163CLXIII
164CLXIV
165CLXV
166CLXVI
167CLXVII
168CLXVIII
169CLXIX
170CLXX
171CLXXI
172CLXXII
173CLXXIII
174CLXXIV
175CLXXV
176CLXXVI
177CLXXVII
178CLXXVIII
179CLXXIX
180CLXXX
181CLXXXI
182CLXXXII
183CLXXXIII
184CLXXXIV
185CLXXXV
186CLXXXVI
187CLXXXVII
188CLXXXVIII
189CLXXXIX
190CXC
191CXCI
192CXCII
193CXCIII
194CXCIV
195CXCV
196CXCVI
197CXCVII
198CXCVIII
199CXCIX
200CC
201CCI
202CCII
203CCIII
204CCIV
205CCV
206CCVI
207CCVII
208CCVIII
209CCIX
210CCX
211CCXI
212CCXII
213CCXIII
214CCXIV
215CCXV
216CCXVI
217CCXVII
218CCXVIII
219CCXIX
220CCXX
221CCXXI
222CCXXII
223CCXXIII
224CCXXIV
225CCXXV
226CCXXVI
227CCXXVII
228CCXXVIII
229CCXXIX
230CCXXX
231CCXXXI
232CCXXXII
233CCXXXIII
234CCXXXIV
235CCXXXV
236CCXXXVI
237CCXXXVII
238CCXXXVIII
239CCXXXIX
240CCXL
241CCXLI
242CCXLII
243CCXLIII
244CCXLIV
245CCXLV
246CCXLVI
247CCXLVII
248CCXLVIII
249CCXLIX
250CCL

Below is a plot showing how the lengths of these Roman numerals changes. As you can see it is very cyclic with the length growing as the digit I is added in stages, then dropping back as this passes a mutiple of five, being replaced by a higher value symbol.

The longest Roman Numeral under 250 is CLXXXVIII which is nine characters long, and represents the numer 188.

The first number to required ten digits is 288, and this is CCLXXXVIII

Multiplication table

Whilst of no practical use, here a heatmap showing the lengths of the product of two Roman Numerals. At the top left is I x I. The lighter color shorts the shorter strings, the darker colors the longer product strings.

Each square to the the right and down increases of number by one. For obvious reasons the chart is symmetric around the leading diagonal, but its interesting to make out the harmonics that make it look like there are rings in the plot. The graph plots products for 1-50 on each axis.

Uses

These days, Roman Numerals are used mainly for garnish, and add an air of sophistication whenever they are used.

They appear on watch and clock faces, in titles of Kings, Queens and Popes, Superbowl and Olympic Games' numbering, as numeric bullets in fancy documents, or as page numbers in book prefaces.

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