History of Numbers
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ScribdTranslationsBolivarian Republic of Venezuela
Ministry of Popular Power for Education
U.E. San Martin School
3rd year Section: "A"
Subject: Mathematics
Subject: Research Work
The History
of the
Numbers
Members:
Milarich Castellanos N 5
Maria Hernandez N 18 Professor:
Keyla Palacios N 22 Luis Moncada
Marian Rodríguez N 27
Caracas, April 3, 2019
Introduction
In thisworkit presents at a very general level the different ways of counting thatthe
manhas invented in itsdevelopmentcultural, since the rudimentary beginnings of the
various civilizations until reaching our present onesystemdecimal. Each cultural
historically has left a legacy for posterity that scientists through
susinvestigationsthey were discovering and understanding their methodologies to operate
mathematically. The operational rudiments are particularly emphasized throughout
of thehistoryand are part of the development of homo sapiens.
Numbers, the way to graphically represent quantities, in a simple manner, the
mental schemes that humanity has followed until achieving counting, assigning to each
an element, a symbol, a graphic, a sound, or a simple mark, are an unknown and not
it has always been the same throughout history.
History of numbers
The history of our numbers is a very ancient story. It is not known for sure.
how long ago humans began to use them, but what we can indeed
To ensure that from the beginning, man needed words to express quantities.
Count how many people were in a cave, express how far the river was, or take
some measure... there was the same need to communicate using numbers that there is today
in day.
People who have studied different languages have found that all have some
idea of numbers, even if it's just the words one and two in their vocabulary. In a tribe in
In Bolivia, there are no specific words to designate numbers except the word 'only.'
used to represent one. In languages where only a few numbers are used, there are
almost no need to express large amounts.
Since there are no written records of when language developed, it is impossible to know.
When did the use of numbers begin? We only know that very early on they
They needed numbers to count. The variety of things used for counting is endless.
from sticks, pebbles, shells, fruits, and knots in a rope, to the universal system of
count with fingers. Another tribe, the Malays, used stones to represent amounts.
when the count exceeded what could be expressed with fingers.
The Sumerians and Babylonians
People spoke for many years before writing began. Likewise,
Many years passed before there were signs for numbers. The first
Documents about written numbers were made about 5000 years ago in the valley.
Asian from Mesopotamia between the Tigris and Euphrates rivers. About 2000 years later, the
The Sumaros, who lived in the same area, developed a numerical writing system.
known as cuneiform. Its use spread and was adapted by Babylonian merchants
who used it for their business records. Using a stick with a pointed tip
of triangle, the Babylonians made impressions on clay tablets that were then fired.
for its preservation.
The Egyptians
The ancient Egyptians lived in Africa, near the Nile River and were also traders.
sellers who needed to keep a record of their transactions. How they came to be very
prosperous, they needed to write large numbers which led to the development of a system
that extended into the millions. As for the symbols used, the Egyptians chose
things in their environment to symbolize categories of numbers in base ten. While in
in our numerical system we read the numbers from left to right, the Egyptians
they alternated from left to right in one line and from right to left in the next
in the same way they plowed their fields.
The Chinese
The oldest known numbers were used by the Chinese and were then
adapted by the Japanese. The system contains symbols for the numbers 1 to 9 and for
the tens, hundreds, and thousands. The Chinese wrote vertically and read from top to bottom.
In a number, the first symbol indicated the quantity of the second symbol and the third
symbol the amount of the room and so on.
Origin of Numbers
Humans have managed to create more or less effective numerical systems.
to be able to progress. Is writing older than numbering? There is no evidence
writing documentary until 2200 BC. From that date are the baked clay tablets.
found in the Babylonian cities of Susa and Uruk, today the Iraqi city of Warka.
Egyptian numbering However, it seems that the Egyptians got ahead in almost a
millennium, since in the times of the first dynasty this people had a system
decimal function that could keep track of up to millions of units. It was given to him
it is called a hieratic numeral system. There existed a series of separate symbols or signs for
each number up to nine and for each power of 10. However, they did not know the
number zero. Egyptian numbering. Thus, the number 4 was four lines and the 10 a 'U'.
inverted. This meant that they had to use more signs than today to express the same ones.
quantities: to write '98' they put eight strokes and nine symbols of the number 10. The
Babylonian numbering The primitive numbering was not decimal, it was not based on
Decade. The Babylonian system, used approximately around 1800 BC, had as
regarding the number 60, and it was for this reason that the counting of time was based on that unit
of measure. Initially, there was no number 0. But it was also the Babylonian numbering.
perfected in the 4th century BC, the one who created the concept and use of the number 0. Could
to be placed at the beginning, that is, to the left. It could also be inserted in the middle of a
quantity, within a given number, but curiously it could not appear at the end. The
Greek numbering Around 500 BC, the Greeks were already using the letters of the
its alphabet. It was called the acrophonic or Attic system. In this way, the letter a = 1. This
A numeral system lacking zeros was used for a thousand years. The Jews first and the Arabs later.
They adapted it to their own alphabets later on. By that time, as there were still no
calculators, calculations were done with the abacus, a manual device consisting of several
rows of small movable stones threaded, from where the term "calculus" derived,
Latin calculus = little stone. Roman numeration The Romans improved the system
numeric by introducing new numbers, such as 5, 50, and 500: that
correspond to the letters V, L and D respectively. They also established a novelty
Important: placing a symbol before or after another of greater value subtracted or
added to this: XL was 50–10, and LX was 50 + 10. But this system of assigning letters
Numerical value made it difficult to perform arithmetic operations and multiply large numbers.
it was impossible to quantify. The Mayan numbering in the Amerindian civilization of the
the base was the number 20: the fingers of the feet and hands. It was the first people in
to employ 0, which was more of a concept than an operational number. Maya numbers
they read bottom to top, wrote in columns, and used base 20. It is not known
graphic representation of its numbering prior to the third century of our era. The word
'Zero' is Sanskrit: from sunya = nothing, and it was indicated with a comma. The Arabs, after knowing
its possibilities called him sifr = empty. Later it was 'Latinized' by Leonardo of
It derives from the term zephirum, from which the Castilian word 'zero' originated. The origin of the
current numbering The Arabic numbering, which is how the numerical system is referred to
what we use today was born in India around the 5th century BC. Something you must
be clear to understand the history of numbers. There is representation of the
numbers 1, 4 and 6 in the Buddhist inscriptions of Ashoka from the 3rd century BC. In others
Inscription from a century later clearly shows the numbers 2, 4, 6, 7, and 9 engraved.
in the monuments of Nana Ghat. Documents from the 2nd century AD already mention all
less than 8. The current numbers appeared in India, where they were invented around the 5th century
the arithmetic of decimal position and the use of 0. The first example of the use of numbering
decimal data from 595, which includes the functional use of 0: a point. It was there that
he started counting from 1 to 10, as we do today. There is concrete reference to the
Indian numbering in a note written by Bishop Severus Sebokht around 650, which
It talks about 'the new signs'. At the end of the 8th century, some tablets were transferred to Baghdad.
astronomical events in which the new numbers could already be seen. In China in the 9th century (see
history of China), the 0 began to be represented in the same way as today: a little circle. From
The Arabs took the system in India. In the year 825, Muhammad ibn Musa al-Khwarizmi.
he published his algebra treatise in Baghdad (from his surname derives the word numeral). The
Al-Khwarizmi's little book would be translated into Latin by Adelard of Bath three centuries later.
In the Spanish city of Córdoba, the novelty was already known in 976. From this year, it
preserve a valuable manuscript that contains the new numerical symbols. It is clear
that these advancements reached the rest of Europe through Spain around the 10th century, a date in
that traveled to Córdoba the French monk Gerbert of Auvergne, who was proclaimed in 999
Pope with the name of Silvester II. He was the Pope who most contributed to spreading the new
numbering, although it took time to establish itself. Arab science, more advanced than Christian science in
the Middle Ages soon made its way, and around 1200 Leonardo of Pisa wrote his Liber
Abaci: the numbering of ten digits was already established. This does not mean that they had
favorable and universal acceptance, as it is known that in Europe in 1300 it was prohibited the
Arabic numerals in commercial transactions because they could be falsified.
numbers with greater ease than Roman numerals. In fact, it was not until 1800 that they were
fully embraced and without reservations.
Characteristics of numbers
NATURAL NUMBERS:
Natural numbers are those that we typically use for counting. They are those
positive numbers and without decimal part.
N = { 1, 2, 3, 4, 5, 6, 7 ... }
INTEGERS:
They are all the natural numbers and their opposites, that is, the positive integers and
negatives.
Z = { 1 , -1 , 2 , -2 , 3 , -3 , 4 , -4... }
RATIONAL NUMBERS:
They are all those that can be written in the form of a fraction. They include natural numbers and integers.
IRRATIONAL NUMBERS:
They are the numbers that have infinite decimal places.
p = 3.141592354....
e = 2.7182818....
REAL NUMBERS:
They include all the numbers previously described. They cover the real line and any point of
this is a real number.
Evolution of numbers
Throughout history, humans have always had the need to tell.
express commercial operations and solve other problems that have arisen in the
development of mathematics.
We will analyze the evolution of the various sets, in such a way that each of them
is contained in the following. However, the evolution of these numbers may be that
coincides in time.
Natural numbers:
Since the beginning of humanity, different cultures have employed various forms
to count, whether using stones, notches on sticks, and even the fingers of the hands and
the feet. However, it was not until the 9th century AD, thanks to Al-Khwarizmi, that
it adopts the Hindu numbering system. However, in Europe we will have to wait.
until the 13th century for natural numbers to arrive. Establishing itself in a way
formal in the 19th century thanks to Peano, to whom we owe the axiomatic definition of the
natural numbers.
The integers:
The solution of equations of the type x+a=b, where a>b, do not have a place in the body of the
natural numbers. We need to expand the set and define numbers in this way.
negatives. These numbers arose from the need to operate with negative quantities,
especially in business operations. The first to introduce the numbers
The negatives were the Hindus, specifically Brahmagupta. They arrived in Europe in the late century.
s.XV thanks to the French mathematician Nicolas Chuquet. However, it was not until the end of the
19th century when Weierstrass outlines the model of integers, defining them
as equivalence classes of pairs of natural numbers.
Rational numbers:
When solving the equation ax = b, such that b is not a multiple of a (that is, a is not
divisor of b), there is no solution in integer numbers. The need to fraction the
unit leads us to the definition of fractions. Although they have been worked with since the
antiquity, but with complicated notations. The Babylonians began to use the
decimal notation, dividing the unit into successive powers of 60. But it was the Arabs
who established the horizontal bar to separate the numerator and the denominator.
The real numbers:
A new obstacle appears that causes the body of rational numbers to remain
small, like finding the measure of the diagonal of a square with side 1, or the result
from the equation x squared equals 2. This discovery occurs thanks to the school
Pythagorean, and were given the name of incommensurable. However, it was not until the
arrival of the Renaissance, when European mathematicians took advantage of the system
decimal, to define irrational numbers as those numbers that have infinite
decimal figures.
Complex numbers:
Finally, as the final obstacle, we encounter a new problem, what happens
when solving a quadratic equation or higher, we obtain a square root
negative? Until then, this equation has no solution (in fact, it has no real solution).
Although work began with these numbers as if they were normal numbers,
since they met a series of conditions. The esoteric nature of these numbers diminished.
eliminating, especially with Cardano's work in 1545 'Arg Magna'. However, it was
Euler is the one who established the notation that we now know to denote the square root of minus one.
How are you?
Conclusion
At the conclusion of this work, we want to convey how important they can become.
numbers, and to make us think that, without them, we would not have been able to progress as we have now.
Because, even if denied, numbers are in our daily life, in different
professions. This work is already finished, but we must be clear that the numbers are
infinite, and they have different concepts, whether they are: Rational Numbers, Natural Numbers,
Complex Numbers, Square Root.
Numbers are what help to modernize humanity, for science is the
it helps, but calculating the numbers and putting the correct ones is what makes it
let's move forward.
Bibliographies