Mathematics in other Cultures Scavenger Hunt
Roman Mathematics
The Roman Republic was the phase of the ancient Roman civilization characterized by a
republican form of government; a period which began with the overthrow of the Roman
monarchy, c. 509 BC, and lasted over 450 years. The Roman Republic was governed by a
complex constitution, which centered on the principles of a separation of powers and checks
and balances.
Symbol
Value
I
1 (one) (unus)
V
5 (five) (quinque)
X
10 (ten) (decem)
L
50 (fifty) (quinquaginta)
Roman numerals, as the name suggests, originated in
ancient Rome. No one is sure when roman numerals were
first used, but they far predate the middle ages. Theories
abound as to the origins of this counting system, but it is
commonly believed to have started with the ancient
Etruscans.
C
100 (one hundred)
(centum)
D
500 (five hundred)
(quingenti)
Roman numerals are based on seven symbols: a stroke
(identified with the letter I) for a unit, a chevron (identified
with the letter V) for a five, a cross-stroke (identified with
the letter X) for a ten, a C (identified as an abbreviation of
Centum) for a hundred,etc...
M
1000 (one thousand)
(mille)
Symbols are iterated to produce multiples of the decimal (1, 10, 100, 1000) values, with V, L, D
substituted for a multiple of five, and the iteration continuing: I "1", II "2", III "3", V "5", VI "6",
VII "7", etc., and the same for other bases: X "10", XX "20", XXX "30", L "50", LXXX "80"; CC
"200", DCC "700", etc. At the fourth iteration, a subtractive principle may be employed, with the
base placed before the higher base: IIII or IV "4", VIIII or IX "9", XXXX or XL "40", LXXXX or XC
"90", CCCC or CD "400", DCCCC or CM "900".
If smaller numbers follow larger numbers, the numbers are added. If a smaller number
precedes a larger number, the smaller number is subtracted from the larger. For example, if
you want to say 1,100 in Roman Numerals, you would say M for 1000 and then put a C after it
for 100; in other words 1,100=MC in Roman Numerals.
Roman Numeral Table
1I
2 II
3 III
4 IV
5V
6 VI
7 VII
8 VIII
9 IX
10 X
11 XI
12 XII
13 XIII
14
15
16
17
18
19
20
21
22
23
24
25
26
XIV
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIV
XXV
XXVI
27
28
29
30
31
40
50
60
70
80
90
100
101
XXVII
XXVIII
XXIX
XXX
XXXI
XL
L
LX
LXX
LXXX
XC
C
CI
150
200
300
400
500
600
700
800
900
1000
1600
1700
1900
CL
CC
CCC
CD
D
DC
DCC
DCCC
CM
M
MDC
MDCC
MCM
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Chronograms
Roman Numerals
I=1
V=5
X = 10
L = 50
C = 100
D = 500
M = 1000
A chronogram is a sentence that has hidden numbers.
Most chronograms are Latin inscriptions on old houses.
You must interpret the capital or highlighted letters I,V,X,L,C,D,M as Roman numerals. The sum
of the numerals is the year it was built.
I.
In the spa museum in Bad Salzuflen, Germany, you can see a joist with two chronograms. In
former times it was above the hall entrance of Georg Schröder's house, Loofher's son-in-law.
The first line is:
GLORIA SIT DEO PAX IN TERRA ET HOMINIBVS BONA VOLVNTAS
(Glory to God, peace on earth and a satisfaction to mankind.)
What year was this structure built?
The second line is:
PRINCIPIVM DEVS AETERNVS FINISQVE BEATVS
(The eternal God is both, the beginning and the blessed end.)
What year is represented in this chronogram?
II
Imprinted on a coin Struck by Gustavus Adolphus is:
ChrIstVs DuX ergo triVMphVs
(Christ the Leader, therefore triumphant)
What year was this coin made?
III
In a work entitled Hugo Grotius his Sophompaneas, the publishing date is
indicated by the author's name:
FranCIs GoLDsMIth.
What year was the book published?
IV.
Many lengthy examples of chronograms can be found in Germany, notably in
and around the town of Bad Salzuflen commemorate the building of houses in the form
of prayers or quotations from the Bible, for instance:
SVRGE O IEHOVA ATQVE DISPERGE INIMICOS TVOS
(Rise, oh Jehovah, and destroy your enemies)
What year was this structure built?
V.
The parish priest Johann Loofher lived in Bad Salzuflen from 1615 to 1660. He designed a
chronostichon for the facade of his house (now Lange Straße 10). It says:
SIT LARIBVS NOSTRIS OPTO CONCORDIA CONSTANS NOSTER ET ASSIDVO LVCEAT IGNE FOCVS
(May this house be given permanent harmony, I wish, and the fire of our stove is to shine in ever lasting gleam.)
What year was his house built?
Answers
I.
Both lines contain the year 1630. The first chronogram comes from the
Christmas Story St.Luke's Gospel 2:14. It is interesting to know that you can
see this biblical saying on the edge of the pulpit roof of St. Kilian's church
at Schötmar/Bad Salzuflen. - The second chronogram is a chronodistichon
II.
This gives us MDCXVVVII or 1627
III.
This gives MDCLII or 1652
IV.
This gives 1625 as the year of building.
V.
The sum of the Roman numerals is:
I+L+I+V+I+C+C+D+I+C+I+D+V+L+V+C+I+C=1621.
The house was built in 1621.