HISTORY OF MATHEMATICS

By :
RAHMAT RISALDY RAMLI
1911442005

DEPARTMENT OF MATHEMATICS

FACULTY OF MATHEMATICS AND SCIENCE

STATE UNIVERSITY OF MAKASSAR

2020
foreword
A fraction is a number consisting of two numeric parts, namely a number as a pembilang
(numerator) and a number as a pembagi (denominator) where the two parts of the number are
separated by a slash symbol (/). In faraid science, this divider is often referred to as the origin
of the problem or the subject matter. The writing format for fractions is as follows: a / b and b ≠
0, where "a" is a numerator and "b" is a denominator. Sometimes this writing format uses an
a
underscore (_) such as: .
b

Formulation of the problem

Learning objectives
- To understand about the history of decimal fractions
- To understand the process of developing decimal fractions
- To find out who created the symbols in decimal fractions
 Decimal Fraction

A. history of decimal fractions

1. Ancient Egypt
The first fractions appeared around 1600 B.C. in an ancient Egyptian relic, Egyptian
papyrus. Uniquely, at that time the ancient Egyptians only recognized the unit fraction, the unit
1 1 1 1
fraction, which was expressed as , where n was a positive integer, for example , , dan
n 2 3 7
(the numerator is always 1). A fraction other than a unit fraction is expressed as the sum of two
2 1 1 1 1
different unit fractions. For example, is expressed as + , it cannot be expressed as + .
7 4 28 7 7
Ancient Egyptian society at that time used a number writing that was different from the
numbers we use today. They have symbols for writing numbers. For example 3 is symbolized as
three horizontal lines, |||. Following are some examples of writing fractions from an Egyptian
papyrus.

Each fraction (unit fraction) is symbolized by an ellipse symbol above the number which is the
value of the denominator (the term pembilang, or numerator, and penyebut, or denominator,
was unknown at that time). The symbol of the person with the foot facing forward on top
means adding the number before the symbol with the number after it. Meanwhile, if the feet
are facing backwards, it means subtracting the previous number from the number after it. The
Egyptians in 1800 BC wrote the base 10 number system with hieroglyphs as written below.
2. Babylonians
Babylonian mathematics refers to the whole mathematics developed by the
Mesopotamian nation (now Iraq) from the beginning of Sumerian to the beginning of Hellenistic
civilization.

It is named "Babilonia Mathematics" because of the main role of the Babikonia region as
a place for learning. In the days of the Hellenistic civilization Babylonian mathematics
combined with Greek and Egyptian mathematics to generate Greek mathematics. In contrast to
the scarcity of sources in Egyptian mathematics, Babylonian Mathematical knowledge is derived
from more than 400 slabs of land excavated since the 1850s. Written in cuneiform writing, the
plates were written when the lat ground was still wet, and burned in a stove or dried in the sun.
Some of them are homemade works.
Most of the known slabs of lat earth date from 1800 to 1600 BC, and cover the topics of
fractions, algebra, quadratic and cubic equations, and calculation of straight numbers,
multiplicative inverse, and twin primes. The plates also include the multiplication table and
methods of solving linear equations and quadratic equations. The Babylonian Plate of 7289 BC
gives an approximation for √ 2 which is accurate to Ima the decimal place.
Babyconia mathematics used the sexagesimal number system (base-60). From here the
substitution of the number 60 seconds for a minute, 60 minutes for an hour, and 360 (60 x 6)
degrees for a circle is derived, as well as the use of seconds and minutes in a circular arc which
represents a fraction of degrees. The Babylonian advances in mathematics were supported by
the fact that 60 had many divisions. Also, unlike the Egyptians, Greeks, and Romans, the
Babylonians had a true place-value system, in which the numbers written in the left column
represent the larger value, as in the decimal system. However, they lack the equivalent decimal
point, and so the place value of a symbol often has to be estimated based on the context.

3. Ancient Greek
 The ancient Greek era is also called the stone age, because at this time humans still use
stone as tools and the remains of human paradigm found at this time include: stone tools,
animal repeated bones, the remains of several plants, drawings in caves, burial place for
ancient human bones. Between the 15th and 6th centuries BC, humans discovered iron,
copper, and silver for various purposes. Fifteenth Century Before Maschi iron was first used in
Iraq, tilak in Europe, China. In the 6th century BC in Greece appeared Fikafat. In ancient
Greece, in the world of knowledge, knowledge was characterized based on know-how which
was based on empirical experience. In addition, numeracy is pursued by means of a
correspondence one-to-one mapping process. An example of how to count the animals that
will enter and leave the cage with gravel. However, at this time humans have begun to pay
attention to the state of the universe as a natural process.
The use of fractions in Ancient Greece was so familiar that they even thought that all
length measurements could be expressed by integer ratios, only they had not used the
symbolism they are today.

4. India

Development and calculation with fractions developed from India. The decimal fraction
writing that underlies our present decimal fraction also comes from India. Around the year 630
A.D, the mathematician from India, namely Brahmagupta who was born in Sind (Pakistan) in
Brahmasphutasiddhanta explained about the writing and calculation of fractions, but not
exactly exactly what we use. He and other Indian mathematicians also expressed a fraction
without a horizontal line separating the numerator and denominator. Even though the
calculation of the fraction is based on the place value (decimal), it has not used decimal writing
as we use.
5. Chinese Nation

In China we can see the jiuzhang suanshu or often translated The Nine Chapters on The
Mathematical Arts (nine chapters on the art of mathematics) have also used place values for
fractions. Even using the idea of the Smallest of alliance certainty. The use of the idea of
decimal fractions itself dates back to the Shang dynasty (around 1800 to 1100 BC)
B. Fractional symbol

1. Al-Qalasadi
Some say that Al-Qalasadi (1412-1486) was the first to write a horizontal line between
the numerator and denominator.

The full name of al-Qalasadi is Abu al-Hasan Ai Muhammad bin al Khurasi al-Basri. He
was born in Baza (Basta), Spain, in the 15th century. In addition to being famous as a
mathematician, Andalusian intellectuals were also known as lawyers At first, al-Qalasadi only
pursued a few subjects of science, such as the science of inheritance (faraid).
he is known as a scholar who is very productive in producing quality works. He was able
to make a variety of themes an interesting subject. Some of his works are so well known and
read by scholars in the West and East. His big name has also soared as a distinctive writer. He
dared to make works that were different from other works of his time.
Al-Qalasadi was the first to use the symbols that are now used in writing fraction
notation equations. As is known, one of the important elements in mathematics, especially
numbers, is a fraction. These symbols were first developed in the 14th century by Ibn-albanna
then in the 15th century developed by al-Qasadi, al-Qasadi introduced mathematical symbols
using characters from the Arabic aphabet. He uses wa which means and for addition (+), for
subtraction (-), al-Qasadi uses illa means "less" while multiplication (X) he uses fi which means
"times". The symbol ala meaning for is used for division (/).
 Apart from that, al-Qalasadi also used the symbol “ j ” to symbolize the "root". The
“ shay “ symbol is used to represent a variable ( x ). Then, he used the symbol “ m ” to represent
"squared" ( x 2). The letter “ k “ is used as the symbol for "cube" ( x 3). Meanwhile, ”
i “ symbolizes the equation (=). Al-Qalasadi breathed his last on December 1, 1486 (15
Dzulhijjah 891 H) in Ifrikiya, Bedja.

2. Al-Kasyi

Meanwhile, the use of decimal fractions and their significant calculation methods is
found in the work of al-Kashi (1380-1429), Miftah al-Hisab (Key to Calculation). This was first
expressed by P. Luckey in 1948.
The name of the word is Ghiyattuddin Jamsyidn bin Mahmud bin Muhammad al-Kasyi or
better known as al-Kasyi or al-Qasyani. He was born in Kashan, a city located in the middle of
Iran, in the late 14th century AD (1380).
Al-Kasyi was the first scientist to use the number zero. He used that number in the
calculation process, which made him succeed in creating decimal fractions. In the field of
astronomy, al-Kasyi succeeded in making stellar monitoring tools, namely a tool used to
determine the positions of various stars. distance from the earth how the eclipse occurs, and
other things related to astronomy.
The discovery of the decimal number and the number zero by a-Kasyi is very useful for
our lives. The positions of the fraction decimal and zero are used in a wide variety of scientific
and commercial fields. What he conveyed was a service for the advancement of mathematics.
He died in the City of Sarmankhan (Ubekistan) on 22 June 1429.
It is now widely recognized that al-Kasyi was the inventor of the decimal fraction.
However, the basics have been introduced before, especially in colleges founded by okeh al-
Karaji or al-Karkhi (953-1019 or 1029), especially al-Samwal (1125-1180). Al-Kasyi itself has not
used a coma for decimal fractions, but uses a sign in the form of the word sha (an Arabic letter),
between the whole number and the fractional part of the decimal.

3. Simon Stevin

The basis for the modern decimal notation was introduced by Simon Stevin. Simon
Stevin (1548/49 1620) was a Flemish mathematician and engineer. He is active in many fields
of science and engineering, both theoretical and practical. He also translated various
mathematical terms into Dutch, making it one of the few European languages where the word
for mathematics, Wiskunde ("the art of what is certain"), is not of Greek origin (via Latin).
Stevin wrote a 36-page booklet entitled De Thiende ('the art of tithing'), first published
in Dutch in 1585 and translated into French as Disme. The full title of the English translation of
Decimal arithmetic: Teaches how to do all any calculations by the whole number without
fractions, by the four common principles of arithmetic: viz. addition, subtraction,
multiplication, and division. The concepts referred to in this booklet include the unit of
Egyptian fractions and fractions.
 Conclusion

If seen from the above discussion, history has proven that the initial fraction numbers
are not uniform or different in each ethnic group, such as: Ancient Egypt, at that time, only
1
recognized unit fractions, fraction units, which were expressed as , where n was an integer.
n
positive. At that time, Babylonians brought down more than 400 clay tablets which were
written in cuneiform writing while the plates were still wet, then burned in a furnace or dried in
the hot sun. The slabs cover the topics of fractions, algebra, quadratic and cubic equations, and
the calculation of twin prime numbers. Greece, which at that time used the calculation with
pebbles. The use of fraction figures in Ancient Greece was so familiar that they even assumed
that all length measurements could be expressed by integer ratios, only they had not used the
symbolism they have today. India at that time thought that the writing and calculation of
fractions was not exactly what we used. Even though the calculation of fractions is based on
the place value (decimal), it has not used decimal writing as we use. The Chinese, who at that
time used the place value for fractions, even used the idea of the smallest common multiple.
Some say that al-Qalasadi (1412-1486) was the first to write a horizontal line between
the numerator and denominator. Meanwhile, Jeff Miller mentioned the name al-Hassar (12th
century).
While the use of decimal fractions and their significant calculation methods are found in
the work of al-Kasyi (k.1380-1429), Miftah al-Hisab (Key to Calculation). This was first expressed
by P. Luckey in 1948. Previously it was often said that the inventor of the decimal fraction was
Simon Stevin (1548-1620), who wrote La Disme in 1585, whereas Francçis Viéte (1540-1603)
himself had previously written about decimal fractions. . It is now widely recognized that al-
Kasyi was the inventor of the decimal fraction. However, the basics have been introduced
before, especially in the colleges founded by al-Karaji or al-Karkhi (953-1019 or 1029), especially
al-Samawal (1125-1180). Al-Kasyi himself has not used a comma for decimal fractions, but uses
a sign in the form of the word sha (an Arabic letter) between the whole number and the
fractional part of the decimal.