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 south-central Asia, and the Hwang Ho and then the Yangtze in eastern Asia, there was ancient nations called the ancient 4-civilizations 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 wedge-shaped 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 wedge-shaped 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 one-to-one 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(104) +3(103) +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=40-2+

Sometime between 3000 and 2000 B.C., the ancient Babylonians evolved a sexagesimal system employing the principle of position.

2(603) + 25(602) + 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.

















This way disabled them from calculating multi-digits number so they used abacus.

The Hindu-Arabic Numeral System: 1,2,3,4,5,6,7,8,9,0
The Hindu-Arabic 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 al-Khwarizmi 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.

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Second Midterm Exam

تفاضل وتكامل 1  يوم الثلاثاء الموافق 19/03/2019

Calculus I Tuesday 19/03/2019

Second Midterm Exam

تفاضل وتكامل 2

يوم الخميس الموافق 21/03/2019

Calculus II Wednesday 21/03/2019

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