History of the development of mathematics in India. Presentation

Description of the presentation for individual slides:

1 slide

Slide Description:

Figures of the peoples of the world Mathematics, being the most ancient of all sciences, at the same time remains eternally young ”(M. Keldysh) Completed by: OD Fedoskina teacher of mathematics MBOU secondary school № 1 Sovetskaya Gavan 2014

2 slide

Slide Description:

"The idea of \u200b\u200bexpressing all numbers in signs, giving them, in addition to meaning in form, also meaning in place, is so simple that it is precisely because of this simplicity that it is difficult to realize how amazing it is" Laplace (1749 - 1827)

3 slide

Slide Description:

Humanity speaks more than 2000 languages. Each nationality has its own language, its own culture. But there is a language that is understandable to every literate person, this is the language of mathematics. Mathematical symbols are the same throughout the world. Any formula, any mathematical expression written using numbers and action signs has the same meaning for all peoples. People did not come to this international language of mathematics right away. The path was long and difficult. People began to count for a long time, even when there was no concept of writing. When counting, apparently, for a very long time, they were limited to the numbers one and two. The number three came later. Many other numbers later appeared. Millennia have passed from the ability to count to the ability to write down numbers. Initially, pebbles, notches on sticks, on trees, knots were compared to oral counts, and gradually they moved to conventional records. Who was the first to write numbers is unknown. In the distant past, the systems of numbers for different peoples at different stages of their cultural development were different.

4 slide

Slide Description:

Egyptian Numbers The ancient numeric records of the Egyptians date back to 3300 BC. Two ancient mathematical papyri have come down to us: the Reind papyrus, written by Ahmes around the 18th - 17th centuries. BC. and an earlier Moscow papyrus. According to papyri and other sources, it is established that the image of numbers in Egypt went through three stages. The number system was decimal

5 slide

Slide Description:

Greek Numbers The ancient Greeks had numeric signs even before the flowering of Greek culture. The original way of writing numerical signs is called Attic, according to the place of its origin, or Herodian, by the name of Herodian (II-III centuries AD), from whose works the signs of numbers are known. According to this system, numbers were indicated by the first letters of their name. This system lasted until the 1st century A.D. About 500 BC. another system of Greek numbering arose - Ionic. In this system, the letters of the alphabet were used to denote numbers, and even those letters that had already fallen out of use by that time. All numbers up to 10, full tens and full hundreds were designated. According to this system, all numbers up to 10 - 1 were recorded. The Ionic system is close to the positional one. Archimedes and Apolonius used this system in their work.

6 slide

Slide Description:

Roman numerals Roman numbering has a very ancient origin. When compiling the numbering, the Romans used the principle of addition, subtraction and partial division. In recording numbers 3-III, 6-VI, the principle of addition is applied. IV-4, IX-9 are written according to the principle of subtraction. The division principle is implemented in writing V-5. This is half of X-10. Roman numbering is decimal, but not positional. There is no zero.

7 slide

Slide Description:

Chinese numbering Chinese culture is one of the oldest cultures in the world. The oldest Chinese book on mathematics dates back to about AD 1000. BC. According to the device of the Suapan calculating device, one can conclude that in ancient China there was a fivefold number system. Until recently, such number signs were used in China.

8 slide

Slide Description:

Numbering of the Maya peoples In central America, on the Yucatan Peninsula, lived the Mayan Indian people, who had in the VI-VIII centuries. AD high culture. This people had two systems of writing numbers. One system was used in everyday life.

9 slide

Slide Description:

The numbering of the Maya peoples The second system was used mainly in calendar calculations and was positional decimal. The numbers were written as in the figure. In the writing of numbers by the Mayan people, you can see the remnants of the fivefold system

10 slide

Slide Description:

Babylonian numerals Babylonian culture is as old as Egyptian. According to numerous excavations carried out in the 19th and 20th centuries. AD A large number of clay tables with numbers have been discovered. These tables have lain in the ground for up to 5,000 years. At first, the Babylonians denoted numbers in the form of holes and circles. The lunochka represented one, and the circle - 10. Later, numbers began to be depicted as wedges. One wedge represented a unit, and two wedges, connected at an angle, represented 10. In the cuneiform sexagesimal system of notation of numbers, the positional principle was implemented. We still use the Babylonian sexagesimal system of counting when the hour is divided by 60 minutes, and the minute by 60 seconds. The same was preserved when dividing the circle.

11 slide

Slide Description:

Slavic numbering The Slavs used decimal alphabetical numbering. A special sign "titlo" was placed above the numbers - letters. To designate large numbers, the Slavs used one letter, framed by a corresponding border. In Russia until the 18th century, Slavic numbering was used. The first mathematical manuscript in Russia appeared in the 12th century. This is "the teaching of Kirik the Deacon and Domesticus of the Anthony Monastery, and they are a man of all age." The numbers in this book were in alphabetical numbering. The decimal positional system appeared in Russia in the 17th century. In Magnitsky's book "Arithmetic, that is, the science of numbers ..." calculations are carried out on Hindu numbers, and the pages are numbered with Old Church Slavonic numbers.

12 slide

Slide Description:

13 slide

Slide Description:

Indian numbering The ancient peoples of India had a very high culture, but there are almost no monuments of ancient mathematics left. Before the emergence of the positional system, karoshti numbers were used in some regions of India. It was a decimal non-positional system. It is believed that the positional number system arose in India no later than the beginning of our era, but such assumptions have not been proven by documents. Which people invented the positional system? Scientists have not yet given an exact answer to this question, but most of them tend to think that the zero and positional number system originated in India.

14 slide

Slide Description:

Indian numbering Various numbering systems existed in different regions of India. One of them has spread throughout the world and is now generally accepted. In it, the numbers were in the form of the initial letters of the corresponding numerals in the ancient Indian language - Sanskrit (the "Devanagari" alphabet). Initially, these signs represented the numbers 1, 2, 3, ..., 9, 10, 20, 30, ..., 90, 100, 1000, other numbers were written with their help. Subsequently, a special sign (bold point or circle) was introduced to indicate an empty digit; the signs for numbers greater than 9 fell out of use, and the devanagari numbering became the local decimal system. By the middle of the 8th century, the positional numbering system was widely used in India. Around this time, it penetrates into other countries (Indochina, China, Tibet, Iran, etc.). A decisive role in the spread of Indian numbering in Arab countries was played by a guide drawn up at the beginning of the 9th century by the Uzbek scholar Muhammad from Khorezm (al-Khwarizmi). It was translated into Latin in Western Europe in the 12th century. In the 13th century, Indian numbering becomes dominant in Italy. In other countries of Western Europe, it was established in the 16th century. The Europeans, who borrowed Indian numbering from the Arabs, called it "Arab". This historically incorrect name is retained to this day. The word "digit" (in Arabic "syfr") is also borrowed from the Arabic language. The form of Indian numerals has undergone many changes. The form in which we write them now was established in the 16th century.

"Recording numbers in number systems" - This form represents the contents of any file. Binary system. 2011 Non-positional systems. Alphabetic systems. The binary number system is used to encode a discrete signal. Babylonian sixties. Hexadecimal system. Unit system. Roman numeral system.

"History of numbers and number systems" - Translation of numbers from one number system to another. For example: 0101101000112 \u003d 0101 1010 0011 \u003d 5A316. Non-positional number systems. Number systems translator. No photo. We Give Advice Only Well-Bred Individuals Accordingly M, D, C, L, X, V, I.

"Conversion of number systems" - Conversion of numbers from the 10th number system to the 2nd. 10. 8. 0123456789. Binary. 01234567.101110.1 method. 2.56.

"Examples of number systems" - 19 \u003d 100112. Positional systems. Topic 1. Introduction. Non-positional systems. - 10.4.1452 \u003d. Alphabetic number system (non-positional). Slavic number system. 2983 \u003d. Roman numeral system. + 500. 1000. Discharges.

"Notation of number systems" - Number system is ... History of numbers and number systems. MINISTRY OF EDUCATION OF THE RUSSIAN FEDERATION Municipal general education Chernopenskaya secondary school. ... Method of writing numbers (1, 221, XIX, 10200). Expanded notation of the number. How did a person write down numbers before? Non-positional (for example: Roman - X I V M, Slavic -?).

"Number systems lesson" - Number systems. Binary arithmetic (8 ss). Are we breaking a circle in 10 SS? The computer operates in a binary number system. How do we represent numbers? Lesson 5. Converting numbers from 2 cc to 10 cc? How does a person work? 111, 555.

There are 23 presentations in total

In the 1st millennium A.D. e. indian
scientists raised the ancient
new math, more
high step. They invented
familiar to us decimal
positional system of writing numbers,
suggested symbols for 10 digits,
laid the foundations for decimal
arithmetic, combinatorics,
various numerical methods,
including trigonometric
calculations.

Among the oldest surviving Indian
texts containing mathematical information are highlighted
a series of religious and philosophical books of the Shulba Sutras. These
the sutras describe the construction of sacrificial altars. Most
the old editions of these books date back to the 6th century BC. e.,
later (until about the 3rd century BC) they are constantly
supplemented. Already these ancient manuscripts contain
rich mathematical information, in its level not
inferior to Babylonian.

Indian numbering (way of writing numbers)
was originally exquisite. In Sanskrit there were
means for naming numbers up to 10 ^ 53. For numbers
Syro-Phoenician was first used
system, and from the VI century BC. e. - spelling "brahmi",
with separate characters for numbers 1-9. Some
altered, these icons became
modern numbers that we
we call Arab, and the Arabs themselves - Indian.

Indian numbering
Numbering (numeratio, from numero-count) is the ancient Indian way of writing numbers

Around 500 AD e. unknown to us Indian
scientists invented the decimal positional
number recording system. In the new system
performing arithmetic operations turned out to be
immeasurably easier than the old, clumsy
letter codes, like the Greeks,
or sexagesimal, like the Babylonians.
In the 7th century, information about this wonderful
invention reached the Christian bishop
Syria North Sebokht, who wrote:
I will not touch on Indian science ... their system
dead reckoning superior to all descriptions. I want
just say that counting is done with
nine characters.

Very soon the introduction of a new
numbers - zero. Scientists disagree
where this idea came to India - from the Greeks,
from China or the Indians invented this important
symbol yourself. First zero code
found in a record dated 876 AD e., it has the form
familiar to us circle.

Zero Image

IX century
VII century
Recorded
ancient Khmer
in figures the date "605
year of the era of Shaq "(683
year): oldest
scratch image
(Sambour, Cambodia)

In Antiquity, fractions were already written to friends
to us: one number over another. but
there was one significant difference. Numerator
was located under the denominator. For the first time so
they began to write fractions in ancient India.

Indians used counting boards
adapted to positional notation. They
developed complete algorithms for all
arithmetic operations, including
extraction of square and cube roots.
Our very term "root" appeared due to the
that the Indian word for "mule" had two
meanings: base and root (plants);
Arabic translators mistakenly chose
the second value, and in this form it got into
Latin translations. Possibly similar
the story happened with the word "sine". For
computation control was used to compare
modulo 9.

Scoring board adapted to
positional notation of numbers

The 5th-6th centuries include
works of Aryabhata,
outstanding
Indian mathematician
and an astronomer. In his work
"Ariabhatiam"
there are many
decisions
computational tasks.
Calculated
approximate
value of number π
π \u003d 62832/20000
Approximately 3.1416

Muhammad ibn Musa al-Khorezmi is a mathematician who used the knowledge of the Indian decimal system in his treatise.

Muhammad ibn Musa al-Khorezmi-mathematician
used in his
treatise knowledge
indian decimal
systems.

In the 7th century, another
famous Indian mathematician
and the astronomer, Brahmagupta.
Starting with Brahmagupta,
Indian mathematicians fluent
handle negative
numbers, interpreting them as debt.
Presumably this idea
came from China. When deciding
equations, however,
negative results
invariably rejected.
Brahmagupta, like Aryabhata,
systematically
used continued fractions,
which theory was lacking in
Greeks.

Indian mathematicians continued to develop
mathematical symbolism, although they went on their own
paths. Reducing the relevant Sanskrit terms to
one syllable, they used them as symbols
unknowns, their degrees and free terms of equations.
For example, multiplication was denoted by the sign zy (from
gunita words, multiplied). Subtraction was indicated by a dot
above the subtracted or the plus symbol to the right of it. If a
there were several unknowns, for certain
assigned conventional colors. Square
the root was designated by the syllable "mu", abbreviation
from the mule (root). For naming degrees
abbreviations of the terms "varga" (square) and
"Ghava" (cube):

In the 7th-8th centuries, Indian mathematical
works are translated into Arabic. Decimal
the system penetrates into the countries of Islam, and through
them, over time - and to Europe.

In the XI century there is a seizure and ruin
Muslims of North India. Scientific life on
long period fades away. Significant
figures of this period can be distinguished Bhaskar,
the author of an astronomical and mathematical treatise
Siddhanta Shiromani. Bhaskara gave
the solution of the Pell equation and the series
other Diophantine equations, advanced
continued fractions and spherical
trigonometry.
x2 - 2y2 \u003d 1

Contents Digits history Roman numerals Mayan numerals Digit Zero Indian numerals Numeral systems Positional numeral system Non-positional numeral system Hexadecimal system Conversion from one system to another Use of numeral systems Translator Addition of numbers of unlimited length Conclusions

History of numbers. Numbers is a system of signs ("letters") for recording numbers ("words") (numeric characters). The word "digit" without specification usually means one of the following ten ("alphabet") characters: (so-called "Arabic numerals"). Combinations of these numbers produce two (or more) digit numbers. There are also many other variants ("alphabets"): Roman numerals (I V X L C D M) Hexadecimal digits (A B C D E F) Mayan numerals (from 0 to 19) in some languages, for example, in Ancient Greek, Hebrew, Church Slavonic, there is a system of writing numbers in letters.

Roman numerals The numbers used by the ancient Romans in their non-positional number system. Natural numbers are written by repeating these numbers. Moreover, if the larger digit is in front of the smaller one, then they are added (the principle of addition), if the smaller one is before the larger one, then the smaller one is subtracted from the larger one (the principle of subtraction). The last rule only applies to avoid repeating the same digit four times. Roman numerals appeared around 500 BC among the Etruscans.

To fix the letter designations of numbers in descending order, there is a mnemonic rule: We Give Juicy Limons, Enough Vsem IX. We Give Advice Only Well-Bred Individuals Accordingly M, D, C, L, X, V, I Number Roman Symbol 1I 5V 10X 50L 100C 500D 1000M

Mayan figures. The positional notation, based on the base 20 number system, was used by the Mayan civilization in pre-Columbian Mesoamerica. Maya numbers were composed of three elements: zero (shell sign), one (dot) and five (horizontal bar). For example, 19 was written as four dots in a horizontal row above three horizontal lines

Numbers over 19 were written vertically from bottom to top in powers of 20. For example: 32 was written as (1) (12) \u003d 1 × as (1) (1) (9) \u003d 1 × × as (12) (0) (5) \u003d 12 × × Images of deities were sometimes also used to write numbers from 1 to 19. Such figures were used extremely rarely, surviving only on a few monumental steles. Third digit (four hundred) Second digit (twenty) First digit (units)

Number Zero The Mayan calendar required the use of a zero to denote an empty digit. The first date that has come down to us with zero (on stele 2 in Chiapa de Corso, Chiapas) is dated 36 BC. e. The calendar contains a detailed image of the three columns on stele 1 in La Mojarra. Left date, i.e. 156 AD e. In the "long count" of the Mayan calendar, a variation of the 20-ary number system was used, in which the second digit could contain only numbers from 0 to 17, after which a one was added to the third digit. Thus, the unit of the third category did not mean 400, but 18 × 20 \u003d 360, which is close to the number of days in a solar year.

Indian numerals It is known from history that in science the Indian origin of the so-called Arabic numerals was recognized only in the 19th century. The first scientist to express this, for that time new, idea was the Russian orientalist Georg Yakovlevich Ker (). Since 1731, Ker served in Moscow as a translator for the Foreign Affairs College. No photo

Use of numbers On coins, Indian numerals first appear in 976 in Spain, where there were direct connections with the Arabs. The earliest Russian coin with Indian numerals dates back to 1654. Slavic numerals last appear on copper coins minted in 1718.

Number systems Number system is a symbolic method of writing numbers, representing numbers using written signs. Number system: gives representations of a set of numbers (integers or real) gives each number a unique representation (or at least a standard representation) that reflects the algebraic and arithmetic structure of numbers. Number systems are divided into positional, non-positional and mixed

Positional number systems In positional number systems, the same numerical sign (digit) in the number recording has different meanings depending on the place (digit) where it is located. The invention of positional numbering based on the local meaning of numbers is attributed to the Sumerians and Babylonians; such numbering was developed by the Hindus and had invaluable consequences in the history of human civilization. These systems include the modern decimal number system, the emergence of which is associated with counting on the fingers. In medieval Europe, it appeared through Italian merchants, who in turn borrowed it from Muslims.

Non-positional number systems In non-positional number systems, the value denoted by a digit does not depend on the position in the number. In this case, the system can impose restrictions on the position of the numbers, for example, so that they are arranged in descending order. These systems include the Roman numeral system.

Hexadecimal numeral system Hexadecimal numeral system (hexadecimal numbers) positional numeral system based on the integer base 16. Typically, hexadecimal digits are decimal digits from 0 to 9 and Latin letters from A to F to denote digits from 15 10, that is (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F). It is widely used in low-level programming, since in modern computers the minimum unit of memory is an 8-bit byte, the values \u200b\u200bof which are conveniently written in two hexadecimal digits. This use began with the IBM / 360 system, until that time they used the octal system.

Converting numbers from one number system to another To convert a hexadecimal number to decimal, this number must be represented as the sum of the products of the powers of the base of the hexadecimal number system by the corresponding digits in the digits of the hexadecimal number. For example: the number 5A3 16 5A3 16 \u003d 3 · · · 16² \u003d 3 · 1 + 10 · 16 + 5 · 256 \u003d To convert a multi-digit binary number to the hexadecimal system, you need to split it into tetrads from right to left and replace each tetrad with the corresponding hexadecimal digit. For example: \u003d \u003d 5A3 16

In programming languages \u200b\u200bDifferent programming languages \u200b\u200buse a different syntax to write hexadecimal numbers: In ADA and VHDL, such numbers are indicated as follows: "16 # 5A3 #". In C and languages \u200b\u200bof similar syntax, for example, in Java, the prefix "0x" is used. Some assemblers use the letter "h" after the number. Moreover, if the number does not start with a decimal digit, then to distinguish it from the names of identifiers, "0" (zero) is put in front: "0FFh" () Pascal and some versions of BASIC use the prefix "$". Some other platforms used the # 5A3 notation, usually one or two byte aligned: # 05A3. Other versions of BASIC use & h to indicate hexadecimal digits. On Unix-like operating systems, non-printable characters on output / input are encoded as 0xCC, where CC is the hexadecimal character code

Numeral Systems Translator Consider the conversion of numbers from decimal to hexadecimal and vice versa. To demonstrate the translation of numbers, a program was written in the Visual Basic language. To transfer from one number system to another, you must enter a number in the appropriate field and click on the command button located next to it. The translation result will be displayed in another field.

Addition of numbers of unlimited length In computer processors, it is possible to carry out arithmetic operations for numbers of limited length. If necessary, arithmetic operations with numbers of arbitrary length can be performed using a special program. To demonstrate the solution, a program was written in the Visual Basic language for summing numbers of unlimited length. Enter the required numbers and click the "+" button. The result will be in the third field.

Conclusions Numbers can be named as special types of written signs. Numbers are historical logograms that serve to briefly denote numbers. To record information about the number of objects, numbers consisting of numbers are used. All number systems are divided into two large groups: positional and non-positional number systems. A binary system is used to encode information in a computer Hexadecimal system is a compact notation of binary numbers A digital coding system is used in programming languages

• What is a number?
• Figures of ancient civilizations

2.1. Numbers in Ancient Egypt

2.2. Mayan figures

2.3. Ancient Greece Numbers

2.4. Ancient China Numbers

What is a number?

The numbers have always been, only the rules for depicting them were different. But the meaning was the same: numbers were depicted using certain signs - numbers .

Numeral is the character involved in writing the number.

Number is a value that is made up of numbers according to certain rules. These rules are called number systems 1.

Throughout the centuries-old history of mankind, there have been many different ways to write a number , some have survived to our times, and some have remained in history.

• Originally man became count on fingers ... The most ancient and simple "calculating machine" has long been the fingers and toes.

Figures of ancient civilizations Numbers in Ancient Egypt

The first written numbers, about which we have reliable evidence, appeared in Egypt and Mesopotamia about 5000 years ago.

In the Egyptian system, the numbers were hieroglyphic symbols ; they represented the numbers 1, 10, 100, etc., up to a million. Numbers that are not multiples of 10 were written by repeating these numbers ... Every digit could be repeated from one to 9 times ... For example, the number 4622 was denoted as follows:

Mayan figures

The ancient Maya independently came to use positional principle. Recording of digital signs forming a number, the Maya led vertically , from bottom to top, as if erecting a certain bookcase of numbers.

Maya believed twenty - they had a vague counting system. Numbers from 1 to 20 were designated dots and dashes.

Ancient Greece Numbers

In ancient Greece, there were two main number systems in circulation - attic (or Herodian) and ionic (it is also Alexandrian or alphabetical).

Attic number system was decimal, used repetitions of collective symbols. Used by the Greeks already by 5 c. BC.

• Trait , denoting one, repeated the required number of times, meant numbers up to four.
• Instead of five strokes, a new symbol was introduced D , the first letter of the word "penta" (five).
• When they got to ten, they introduced a new symbol D , the first letter of the word "deck" (ten). T
• New symbols for each new power of 10: symbol H meant 100 (hecaton), X - 1000 (chilioi), symbol M - 10000 (myrioi or myriad). Numbers 6, 7, 8, 9 were designated by combinations of these signs:

Ionic number system – alphabetical. Widespread at the beginning of the Alexandrian era.

• To distinguish numbers from words, the Greeks placed above the corresponding letter horizontal line.
• Similarity greek letter O with modern designation scratch can
• Writing in alphabetic characters could be done in any order, since the number was obtained as the sum of the values \u200b\u200bof individual letters.

Ancient China Numbers

This numbering is one of oldest and most progressive ... This numbering about 4,000 thousand years ago in China.

• The digits of the number were recorded starting with larger values \u200b\u200band ending with smaller ones.
• If there were no tens, units, or some other category, then nothing was put at first and moved on to the next category .
• In order not to confuse the discharges, we used several service hieroglyphs , written after the main hieroglyph, and showing what meaning the hieroglyph-digit takes in this category.

- 1 000;

Such a number record multiplicative , that is, it uses

multiplication:

1 x 1,000 and 5 x 100 + 4 x 10 + 8

Slavic Cyrillic numbering

This form of writing numbers received a large spread due to the fact that it had a complete resemblance to greek notation for numbers ... If you look closely, we will see that after "and" letter goes "in" , but not "B" as follows slavic alphabet , that is, only the letters that are in the Greek alphabet are used.

To distinguish between letters and numbers, a special icon was placed above the numbers - titlo (~)

Roman numbering

The ancient Romans invented the system calculus based on using letters to display numbers. Each letter had a different meaning, each number corresponded to the position number of the letter.

Roman numbering

To read a Roman numeral, there are five basic rules to follow:

• Letters are written from left to right, starting with the highest value.
• Letters I. X. C and M can be repeated until three times in a row.
• Letters V. L. D cannot be repeated.
• Numbers 6, 8, 40, 80, 800 should be written by combining letters: VII (6), VIII (8), XL (40), LXXX (80), CD (400), DCCC (800).

• The horizontal line above the letter increases its value by 1000 times.

then XV (15), CCXLIII (243), ZCXV (2115)

then III (3), XX (20), CCC (300), MCCXXX (1320)

V (5000), CIII (103000), IXDL (9550)

3.1. Indian numbering

3.2. The contribution of Muslims to the development of our number system

3.3. Modern number system

3.4. What is our number system

3.4. Comparison of recording numbers among different peoples

“We call invented indians and numbers 1, 2,. ... ... , 9 and zero arab , since they borrowed them from the Arabs, but the Arabs themselves called these numbers Indian, and arithmetic, based on the decimal system - “ indian account "(Hisabal - Hind).

In the valley Indus there was a civilization, one of the centers of which was a city excavated near the Mohenjo - Daro hills. This civilization, founded by the original population of India, was destroyed by the Aryan tribes of the Rus who came from the Himalayas ...

[Aryan] priests brought with them Vedic worldview and wrote down the sacred books brahmanas "Vedas" ("Knowledge"). They also created invoice recording system. By the 7th - 5th centuries. BC e. the first Indian shiftable mathematical monuments belong ... Most of the scientific treatises of the Indians are written in sanskrit - the language of the religious books of the Brahmins. This language united the numerous peoples of India who spoke different languages \u200b\u200b"

Indian numbering

Integer counting in India since ancient [Aryan] times wore decimal character . Sanskrit - Indo-European language, Similar to ours: 1 - eka, 2 - dwi, \u200b\u200b3 - three .

Indian numbering

Along with digital recording in India was widely used verbal notation of numbers , this was facilitated by the Sanskrit language, rich in its vocabulary, which has many synonyms:

• zero indicated by the words “Empty”, “sky”, “hole”; unit Moon, Earth ; deuce - in words ; four - in words "Oceans", "cardinal points" etc.
• zero indicated by the words “Empty”, “sky”, “hole”;
• unit - items available only in the singular: Moon, Earth ;
• deuce - in words "Twins", "eyes", "nostrils", "lips" ;
• four - in words "Oceans", "cardinal points" etc.

Indian numbering

Application positional principle in verbal numbering , in which the same word, depending on the place, has a different numerical value, and the names of the categories are omitted, was fixed in the 5th century. For example, the number 1021 was written with the words "Moon - hole - wings - Moon".

Indian numbering

Based on numbers brahmi worked out with modern Indian numerals « devaeagari » ( divine letter ), used in the decimal positional system, from which the decimal positional systems of the Arabs and Europeans are derived.