Oriental Mathemati
The Oriental Mathematics: Practical Arithmetic and Mensuration









Characteristic of Orient Mathematics
In the Nile in Africa, the Tigris and Euphrates in western Asia, the Indus and then the Ganges in southcentral Asia, and the Hwang Ho and then the Yangtze in eastern Asia, there was ancient nations called the ancient 4civilizations until 2000 B.C.
The major economic activities of the
ancient nations was to manage their farmlands and to control their
products. Thus, early mathematics can
be said to have originated in certain areas of the ancient Orient (the world
east of Greece) primarily as a practical science to assist in agriculture,
engineering, and business pursuits that is the initial emphasis of the early
mathematics was on practical arithmetic and mensuration.
Algebra ultimately evolved from
arithmetic and the beginnings of theoretical geometry grew out of mensuration. However that in all ancient Oriental mathematics one cannot find even a single
instance of what we today call a demonstration, and one cannot find the reason
to get the answer so to speak 'Do it this way' then 'Get the answer'. That is
many difference from ancient Greek mathematics. Mathematics was one of the essential
parts in the ancient civilization. Today the only record is the
Egypt and Babylonia's. Finally, the orient mathematics could not be
developed because it was a 'living mathematics'.
The Babylonians used imperishable
baked clay tablets and the Egyptians used stone and papyrus, the latter
fortunately being long lasting because of the unusually dry climate of the
region. But the early Chinese and Indians used very perishable
media like bark and bamboo. Thus, although a fair quantity of
define information is now known about the science and the mathematics of
ancient Babylonia and Egypt, very little is known with any degree of certainty
about these studies in ancient China and India.
Babylonian Mathematics
The early
Babylonians drew isosceles triangle on wet clay plates with
needles. In this way, they made wedgeshaped
letters. After making cuneiform the
baked the plates to keep them for a long time.
These plates were excavated at the
Dynasty of King Hammurabi's era, about 1600 B.C. After deciphering
the wedgeshaped letters, we can know that the Babylonians used very high system
of calculation in commerce and agriculture with the sexagesimal positional
system. Babylonian
geometry is intimately related to practical mensuration. The chief
feature of Babylonian geometry is algebraic character. Babylonians already knew the
solution of quadratic equations and equations of second degree with two
unknowns and they could also handle equations of the third and fourth degree.
Thus the development of algebra quickened. We
and undoubtedly owe to the ancient Babylonians our present division of the
circumference of a circle into 360 equal parts.
Egyptian Mathematics
Using a kind
of reed,papyrus Egyptians made
papers. About 1650 B.C. in 'Ahmes' Papyrus' which was written Ahmes,
we can see how to calculate the fraction and the superficial measure of
farmland.
Ancient Egyptians say that the area
of a circle is repeatedly taken as equal to that of the square of 8/9 of the
diameter.
They also extracted the volume of a
right cylinder and the area of a triangle but they handled only a simple
equation.
Marking of Number
Probably the earliest way of keeping a count was by some simple tally method, employing the principle of onetoone correspondence. In keeping a count on sheep, for example, one finger per sheep could be turned under. Counts could also be maintained by making collections of pebbles or sticks, by making scratches in the dirt or on a stone, by cutting notches in a piece of wood, or by tying knots in a string. As the way of counting, people should learn how to mark the numbers. Each nation, therefore, used its peculiar marking of numbers.
The
Egyptian Hieroglyphic: The Egyptian
hieroglyphic numeral system is based on the
scale of 10 and it was used about 3400 B.C.
Any number is now expressed by using
these symbols additively, each symbol being repeated the required number of
times. Thus,
1(10^{4}) +3(10^{3}) +1(10) +5=13015
The Babylonian Cuneiform: This was used from 2000 to 200 B.C. and it simply the marking of numbers using the symbol ''(minus)
Thus, 38=402+
Sometime between 3000 and 2000 B.C.,
the ancient Babylonians evolved a sexagesimal system employing
the principle of position.
2(60^{3}) + 25(60^{2}) + 42(60) + 31 = 524,551
This method is the start of positional numeral system but the Babylonians had difficulties because there was no '0'(zero) until about 300 B.C.
The Mayan Numeral System: This Mayan Numeral System has a symbol for '0' and is based on vigesimal. This is written very simply by dots and dashes.
An example of a larger number, written in the vertical Mayan manner, is shown below.
The rule of
calculation for complex multiplication and division which are used in primary
arithmetic was developed in late 15th century.
The reason why this rule was
developed so late is there were no plenty of papers to record on (Chinese way
of making papers was introduced in Europe after 12th century). They used abacus to overcome this difficulty.
Our present addition and subtraction
patterns, along with the concepts of "carrying over" and
"borrowing" may have originated in the processes for carrying out
these operations on the abacus.
The Roman numeral System: Numeral system was decimal system or binary, the subtractive principle, in which a symbol for a smaller unit placed before a symbol for a larger unit means the difference of the two units, was used only sparingly in ancient and medieval times.
1 
5 
10 
50 
100 
500 
1000 
I 
V 
X 
L 
C 
D 
M 
Thus,
1944=MDCCCCXXXXIIII
1994=MCMXLIV
This way disabled them from
calculating multidigits number so they used abacus.
The
HinduArabic Numeral System:
1,2,3,4,5,6,7,8,9,0
The HinduArabic
numeral system is named after the Hindus, who may have invented it, and
after the Arabs, who transmitted it to Western Europe. The Persian
mathematician alKhwarizmi describes such a completed Hindu system used
position value or 0(zero) in a book of A.D. 825.
It is not certain when this numeral
system transmitted to Europe but this system was used all over the Europe about
13th century.
The dispute between the abacus and
the algorism went on. Finally, the abacus disappeared in 18th
century.
Our word zero probably comes from the Latinized form zephyr of the Arabic sifr,
which in turn is a translation of the Hindu sunya, meaning
"void" of "empty."
By virtue of the symbol of '0' the
decimal system was established. And so we can use four operations
more freely than ever.