ROME BY JUSTIN CORFIELD Th e system of numbers and counting used in Rome and the Roman Empire was developed from Etruscan numerals.. Although there are only a few archaeological fi nds t
Trang 1their sum is a square”), but their solutions lack general
ap-plication or formal proof
Mathematics came to hold tremendous symbolic
impor-tance in Greek culture Pythagoras saw in numbers a model for
the underlying harmony of the universe, and the mysticism of
his worldview infl uenced many later philosophers, including
Plato Th e famous story that the entrance to Plato’s Academy
bore the inscription “Let no one who is ignorant of geometry
enter” may be of doubtful authenticity; nevertheless, it refl ects
well the Platonic attitude toward the centrality of mathematics
in the education of the ideal citizen or philosopher
ROME
BY JUSTIN CORFIELD
Th e system of numbers and counting used in Rome and the
Roman Empire was developed from Etruscan numerals
Th ese numerals, in turn, were adapted from the Greek
At-tic numerals Although there are only a few archaeological
fi nds that have Etruscan numerals, there are enough to show
that the letter I represented 1, an inverted V represented 5,
and X represented 10 Th e fi rst two of these fi gures can be
seen on surviving Etruscan six-sided dice, on which the
op-posite sides add up to seven, as in the dice of today Several
Roman dice also have survived, again with the opposite sides
adding up to seven Six small ivory dice were found at
Pom-peii, all the numbers denoted with small dots; the Romans
oft en played with two dice as opposed to the Greek system, in
which three dice were used
It has been suggested that the original use of numbers
possibly came from notches on a tally stick, with the Romans
using a V for 5 Apart from the ordinary people who needed
to count out money and commodities as well as tell time
and work out the calendar, the Romans also had tax
collec-tors and mathematicians who needed to use larger numbers
Th e Romans used the letters I for 1, V for 5, X for 10, L for
50, C for 100, D for 500, and M for 1,000; they also indicated
large numbers by placing a bar over a numeral to indicate a
numeral in the thousands Above one million there was no
standard format, with fi ve million denoted either by placing a
double bar over a letter V or by underlining, as in V.
Th ere is confl icting evidence regarding the use of some
Roman numerals, especially subtractive ones, whereby IV
represents one less than 5 (that is, 4) Older Roman material
tends to have IIII for 4, making mathematics easier However,
gradually the subtractive notion tended to be used more and
more, eventually becoming the accepted form despite the fact
that IV was also similar to initials representing the god
Jupi-ter (the name in Latin being IVPITER)
It was also from Roman numerals that the number 666
became known as the devil’s number In Roman numerals
666 was represented by the letters DCLXVI, using every basic
numeral except the letter M Th ose familiar with this
phe-nomenon must have seen a bad omen when the Great Fire of
London broke out in 1666 (MDCLXVI)
Interestingly, the Romans did not have a concept of a zero Indeed the fi rst Roman mathematician who is known
to have used the concept was Dionysius Exiguus in 525 c.e., though it seems probable that the concept of zero was in use before then Later the letter N for nullus (nothing) was used
to denote zero
While many Greek mathematicians are household names, there are no details about Roman mathematicians, and it seems likely that the Romans had little interest in pure mathematics Indeed, it was said to have been a Roman soldier who killed the Greek mathematician Archimedes of Syracuse
in 212 b.c.e., and most mathematicians in the Roman Em-pire, such as Diophantus of Alexandria, were actually Greek However, the Romans must certainly have had people who studied applied mathematics to work out architectural plans, load bearings, astronomy, and the supervision of the raising
of revenue Th e poor notation of the Roman numbers did, however, handicap any major advances in mathematics For counting, the Romans used small bronze counters on occa-sions, these having on them pictures of hands with a particu-lar number of fi ngers raised Cicero refers to these counters, which eff ectively were early “counting boards.” Gradually the Romans started using the abacus for more complicated sums, the abacus also oft en being called a “counting board.” Many mathematical instruments have been found in the excava-tions at Pompeii
Surviving surveying manuals show the combination
of arithmetic, geometry, and optics for the Romans’ work Weights and measures followed what now appear to have been arbitrary calculations but must have had some mean-ing at the time For example, the pes, a Roman foot (in
mea-surement), was just over 11.5 inches, making their pace 4 feet, 10.25 inches With a thousand of these feet making a Roman mile, the mile was 1,618 yards Roman numerals have been used many times since the ancient world; they are regularly found in Christian ecclesiastical documents and in European accounts and are still used in calendars, clocks, and watches
THE AMERICAS
BY PENELOPE OJEDA DE HUALA Very little information exists regarding the function of num-bers and counting in the ancient Americas We know that the inhabitants of the Americas probably used the lunar and solar cycles to track the change of seasons, as these changes were vital to their survival Archaeological remains show evidence
of early engineering, which required forms of mathematics However, by the time of European contact, numbering sys-tems existed throughout the Americas
Th e Archaic Period (7000–1800 b.c.e.) in North America saw a near extinction of big-game animals, forcing native groups to rely on local resources to supplement their diets While full-scale agriculture would not be introduced until about 800 c.e., around 3000 b.c.e some forms of early cul-tivation occurred throughout North America Agricultural
numbers and counting: The Americas 805