modern civilization is simply impossible to imagine without numbers.We face them every day, they produce over tens, hundreds and thousands of actions by means of computers.We are so used to it that the history of numbers we are not interested in, and much of it is simply never thought of.But without the knowledge of the past can never understand the present, and therefore you should always strive to comprehend the origins.
So what is the history of numbers?When they emerged, as a man came to their creation?Let us know about it!
Development
In mathematics, there is no more important component.Despite this, the number of the concept has evolved over thousands of years is not the same as the minds of scientists around the world have not agreed yet on how to treat it.
first applied disciplines that are strongly demanded the appearance of the concept, were related to agriculture, construction and stargazing.In turn, the study of the sky and the classification of all measurements are vital for the development of navigation and international trade, without which it could not develop any state.
little philosophy
Even the most primitive figures were worked out and lead to a common mind for centuries.Many of them are the result of a creative rethinking of words or individual letters.The famous Pythagoras said that the numbers are so mysterious, ephemeral substance, which is formed of the whole universe.In general, according to modern concepts of science, he was largely right.
Chinese divided the number into two broad categories (which have been preserved to this day):
- Odd or Yang.In ancient Chinese philosophy they symbolize the sky and supportive.
- Accordingly, even (Yin).This concept symbolizing the earth and instability.
Since ancient times ...
You've probably already guessed that the history of numbers begins its countdown since the days of antiquity.At that time, mysterious symbols were available to only a privileged understanding of the priests, who became the first in the history of our world mathematicians.
Anthropologists and archaeologists have firmly established that a person could be considered as early as the Stone Age.Initially, the first number indicates the number of extremely fingers and toes.To use them for counting steps, production, enemies ... At first, people need only a few simple numbers, but the development of society require increasingly complex systems.This not only led to the development of the rudiments of mathematics, but also contributed to the development of human civilization in general, as demanded by the stress of intellectual work.
So the story of the emergence and development are inextricably linked with the improvement of the mind and the desire of our ancestors to self-improvement.The more they looked at the stars, the more thought about the mathematical regularities (even at a primitive level) in the world around them, the wiser you become.
intuitive notion of including
As soon as there was the first barter, people started to learn to compare the amount of certain items with the same values for the goods offered to him.The notion of "more", "less", "equal", "the same amount."Knowledge quickly becomes complicated, and soon became necessary because the system account.
It should be remembered that the history of the reality of the numbers began with the first appearance of a reasonable person.He intuitively knew how to compare the number of people, animals, objects, still not having a clue about even the simplest math.But that's the strange thing was: any object can be touched, and a number of them and does easily folded in a heap.
The numbers that describe the properties of these same items exist, but to touch or to compare them was impossible.This property has led people in awe, they attributed magical numbers, supernatural quality.
Some evidence hypotheses
Scientists have long assumed that initially only three people have used the concept of "one", "two" and "many."This hypothesis is brilliantly supported by the fact that in many ancient languages, there is the three forms (in Greek, for example): singular, dual and plural.A little later, a man learned to distinguish, for example, two of three bison.Initially, the bill was linked to any particular set of items.
Until recently, indigenous Australians and Polynesians were only two numerals: "one" and "two", and all the rest of the people were prepared by combining them.For example, the number three - two and one, four - two and two.It is remarkably similar to the binary number system, which is now using computer technology!However, the harsh life of those times forced to learn, and so primitive by quickly turned into a mathematical science.
Babylon and Mesopotamia
In ancient Babylon mathematics turned particularly well, because in this state to create gigantic, highly complex structures, which was impossible without computing to build.Oddly enough, but the Babylonians did not feed special thrill to the numbers, so that the history of the development of concepts in the broadest sense of the word began precisely with them.
Babylonians spared all his contemporaries that can record the maximum number of objects, people and animals a minimum set of characters.They introduced the first positioning system, which involves a different numerical value of the same figures, occupying different positions in a numeric context.
In addition, their system of calculation was based on sexagesimal method of measurement, which the Babylonians, as scientists assume, borrowed from the Sumerian civilization.Do not think, though in the field of the history of the concept of a stop.We still use the concept of 60 minutes, 60 seconds, 360 degrees in the context of measuring the circumference.
anticipated Pythagoras
ancient scribes in Babylonia already well known properties of right triangles.In addition, they performed the calculation of the volume of a truncated pyramid.Today, it is known that the history of rational numbers originates from the time it is: Mathematics Mesopotamia and Babylon is not only actively used fractions, but could even use them to solve problems involving up to three unknown values!
In the past, modern mathematicians were surprised to learn that their ancient predecessors succeeded in removing not only the square, but even the cube root.They also came close to the definition of pi, roughly rounding it down to three.It should be noted that the Egyptians later managed much more accurately calculate the value (3.16).
Natural numbers
Equally ancient is the history of the development of a natural number.It is now believed that the first use of this term in his writings, Roman scholar Boethius (480-524 gg.), But long before he Nicomachus of Gerazy wrote in his writings on natural, natural series of numbers.
However, in the modern sense of the term "natural number" is used only to D'Alembert (1717-1783 gg.).But we should not quibble: the very study of the account begins with them.It is called the natural numbers 1, 2, 3, 4, ...
With their appearance was an important step towards the emergence of mathematics and algebra in the form in which we know them today.Modern mathematics confidently speak of an infinite series of natural numbers.Of course, in ancient times, people did not know about.The amount that people simply could not imagine, denoted by the word "darkness", "Legion", "set", and so on.So the history of the development of the line is very old ...
set theory
first natural numbers was extremely short.But the famous Archimedes (III century. BC. E.) Was able to significantly expand this concept.It was this legendary scientist wrote the work "The Sand Reckoner" which his contemporaries often referred to as "Calculation of grains of sand."He accurately calculated the amount of tiny particles that could theoretically take up the entire volume of a sphere with a diameter 15,000,000,000,000 kilometers.
Before Archimedes Greeks managed to get to the myriad of 10,000,000.Myriads, however, they called the number at 10 000. The very name comes from the Greek "Miros", which translated into Russian means "infinitely large", "incredibly great".Archimedes also went further: he started to use in their calculations the term "myriads of myriads," which subsequently led him to create his own, author's calculation system.
maximum value that could be described scientist 80,000,000,000,000,000 contains zeros.If this number is printed on a long paper tape, then it is possible to encircle the globe at the equator more than two million times.
Thus, all positive integers there are two major functions:
- They can be characterized by the amount of any items.
- With their help describe attributes of objects in the number series.
Actual number
But what about the history of the development of the real numbers?After all, in mathematics they occupy no less important place!First, refresh the memory.It can truly be called any positive, negative, and zero.They are divided into a plurality of rational and irrational.
If you carefully read the article, you might guess that the story of the real numbers begins with the dawn of humanity.Since the concept of zero was the first time (more or less reliable information) formulated in the year 876 after Christ, and introduced in India, you can mark this date as an intermediate.
As for the negative, the first time they described Diophantus (Greece) in the third century AD, but "legalized" they were only in India, almost simultaneously with the concept of "zero".
It should be remembered that the history of numbers in mathematics requires them to exist in ancient Egypt as a result of calculations are often manifested.Here are just at the time they were considered "impossible" and "unrealistic", though occasionally used as intermediate values.
Rational numbers
Recall that a rational number is a fraction.In the form of the numerator it uses an integer, and the denominator the number of positive acts.We never know when and where this notion came the first time, but they are actively using the Sumerians already for several thousand years before our era.Their example was followed by the Greeks and Egyptians.
Complex numbers
But they have received recently, immediately after identifying ways to calculate the roots of a cubic equation.I did this Italian Niccolo Fontana Tartaglia (1499-1557 gg.) About the early sixteenth century.And then he found out that to solve all sorts of problems do not always get to use only real numbers.
explain this strange phenomenon was possible only in 1572.Make it could Rafael Bombelli, from which begins the story of the development of complex numbers.But his results for a long time considered to be "fabrications charlatan," and only in the 19th century the great mathematician Carl Friedrich Gauss proved that his distant predecessor was absolutely right.
Another theory
Some researchers say that the first imaginary values were mentioned as early as 1545.It happened in the pages of the well-known at the time of labor "Great art, or Algebraic Rules" Gerolamo Cardano who wrote.Then he tried to find a solution to the problem of the two numbers that when multiplied by 10 give, and in multiplying their value increases to 40.
long time before by mathematicians was the question of whether there can be a lot of them is completely closed.Let us explain: is the operation of complex values result in a complex just real results or further research may lead to the discovery of something entirely new?However, the solution to this problem is in the works of Abraham de Moivre (they date back to 1707), as well as in the writings of Roger Cotes, which were published in 1722.
That's the whole history of the number.Briefly, of course, but the article is still considering the major milestones of research in this area.
