Babylonian number system presentation. Babylonian number system

Material
for the curious

Babylonian number system

The idea of assigning different values to numbers depending on their position in the number record first appeared in Ancient Babylon around the 3rd millennium BC.

Many clay tablets of Ancient Babylon have survived to this day, on which complex problems were solved, such as calculating roots, finding the volume of a pyramid, etc. To record numbers, the Babylonians used only two signs: a vertical wedge (units) and a horizontal wedge (tens). All numbers from 1 to 59 were written using these signs, as in the usual hieroglyphic system.

The entire number as a whole was written in the positional number system with base 60. Let us explain this with examples.

Record denoted 6 60 + 3 = 363, just as our notation 63 denotes 6 10 + 3.

Record designated 32 60 + 52 = = 1972; record meant 1 60 60 + 2 60 + + 4 = 3724.

The Babylonians also had a sign that played the role of a zero. They denoted the absence of intermediate categories. But the absence of junior ranks was not indicated in any way. So, the number could mean 3, and 180 = 3 60 and 10 800 = 3 60 60 and so on. Such numbers could be distinguished only by meaning.

History of numbers and number systems Number systems A number system is a way of writing numbers using special characters - numbers. Numbers: 123, 45678, 1010011, CXL Digits: 0, 1, 2, ... I, V, X, L, ... The alphabet is a set of numbers. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Types of number systems: – non-positional – the value of a digit does not depend on its place (position) in the number record; – positional – the meaning of a digit depends on its place (position) in the number notation; Non-positional number systems Unary number system Unary - one digit denotes one (1 day, 1 stone, 1 ram, ...) At excavations of sites of ancient people, archaeologists find images in the form of serifs, dashes on hard surfaces: stone, clay, wood - that’s what they thought our ancestors some objects, bags, livestock. Ancient Egyptian decimal non-positional system Try to recognize and read this number? 2521 Roman numeral system I – 1 (finger), V – 5 (open palm, 5 fingers), X – 10 (two palms), L – 50, C – 100 (Centum), D – 500 (Demimille), M – 1000 (Mille) Rules: – (usually) do not put more than three identical digits in a row – if the lowest digit (only one!) is to the left of the highest one, it is subtracted from the sum (partially non-positional!) Example: 2381 = M M C C C L X X X I Alphabetic number systems Slavic system numbering Positional number systems Duodecimal system In Rus', counting was done by dozens, remember what a DOZEN is equal to? 12 Where else do we find the duodecimal number system? A year is 12 months, half a day is 12 hours, sets and cutlery are designed for 12 people. Babylonian sexagesimal system Numbers in this number system were composed of two types of signs: a straight wedge served to designate units, and a recumbent wedge - to designate tens. The number 32, for example, was written like this: The signs and served as numbers in this system. The number 60 was again denoted by the same sign as 1, and the numbers 3600, 216000 and all other powers of 60 were denoted by the same sign. Therefore, the Babylonian number system was called sexagesimal. To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. A new discharge began with the appearance of a straight wedge after a recumbent one, if we consider the number from right to left. The decimal system appeared in India in \/ century AD. and it arose after the appearance of the number 0, which was invented by Greek astronomers to indicate the missing quantity. Subsequently, the Arabs became acquainted with this number system. They appreciated it, began to use it, and brought it to Europe in the 12th century. And since that time, humanity has been using this number system. Decimal 0,1,2,3,4,5,6,7,8,9 Binary system With the advent of information science and computer technology, the 2nd number system, whose roots go back to ancient China, found its application. What is the base of this number system? What numbers are used in the recording? 2, numbers – 0 and 1. Why is it used in computer science? Associated with information encoding: recording on disk, transmission of electrical signals. Binary 2 0.1 Clock in the binary number system “BREAKING” your head Read the poem by A.N. Starikov: She was 1100 years old, She went to the 101st grade, She carried 100 books in her briefcase All this is true, not nonsense. When, dusting with a dozen legs, She walked along the road, A puppy with one tail, but 100 legs, always ran behind her. She caught every sound with Her 10 ears, And 10 tanned hands held the briefcase and leash. And 10 dark blue eyes looked at the world as usual... But everything will become completely ordinary, When you understand our story. Did you understand the poet's story? 11002 =1210; 1012 = 510 1002 = 410 102 = 210 Entertaining problem The monkey hangs on its tail and chews bananas. There are 101 bananas in each hand, and 1 more banana in each leg than in the hand. How many bananas does a monkey have? Thank you for your attention

Babylonian sexagesimal system Two thousand years BC, in another great civilization - Babylonian - people wrote down numbers differently. Numbers in this number system were made up of two types of signs: Straight wedge Straight wedge (used to denote units) Reclining wedge Recumbent wedge (to denote tens) Number 60 Number 60 was denoted by the same sign as 1

To determine the value of a number, it was necessary to divide the image of the number into digits from right to left. The alternation of groups of identical characters (“digits”) corresponded to the alternation of digits: The value of a number was determined by the values of its constituent “digits,” but taking into account the fact that the “digits” in each subsequent digit meant 60 times more than the same “digits” in the previous digit .

1. Number Number 92 = written like this: 2. Number Number 444 had the form: FOR EXAMPLE: 444 = 7* The number consists of two digits

To determine the absolute value of a number, additional information was required. Subsequently, the Babylonians introduced a special symbol to denote the missing sexdecimal place, which corresponds in the decimal system to the appearance of the number 0 in the number record. The number 3632 was written like this: This symbol was usually not placed at the end of the number. The Babylonians never memorized the multiplication tables, because... it was almost impossible to do this. When making calculations, they used ready-made multiplication tables.

Babylonian sexagesimal The Babylonian sexagesimal system is the first number system known to us based on the positional principle. The Babylonian system played a major role in the development of mathematics and astronomy, and traces of it have survived to this day. So, we still divide an hour into 60 minutes, and a minute into 60 seconds. We divide the circle into 360 parts (degrees).

ROMAN SYSTEM The Roman system uses the capital Latin letters I, V, X, L, C, D and M (respectively) to represent the numbers 1, 5, 10, 50, 100, 500 and 1000, which are the “digits” of that number system. A number in the Roman numeral system is designated by a set of consecutive “digits”.

DECIMAL NUMERATION SYSTEM Ten different symbols are used to write numbers: numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Once upon a time, the writing of numbers was like this: This representation of decimal numbers is not accidental. Each number represents a number corresponding to the number of angles in it.

YASAC LETTERS In ancient times in Rus', number systems vaguely reminiscent of the Roman ones were widely used among the common people. With their help, tax collectors filled out tax payment receipts - yasaka (yasak letters) and made entries in the tax notebook. kopeck ten kopecks one ruble ten rubles one hundred rubles 232 rubles 24 kopecks

Babylonian number system

Six-decimal Babylonian system -
the first number system known to us,
BASED ON A PRINCIPLE.
The idea is to write numbers in different quantities
depending on what position you have
occupied in the recording of numbers, first appeared in III
T y s i h e l e t i i B.C. in Mesopotamia (Between Rivers)
u shumers. From them it passed to the Babylonians, the new owners of Mezh Fools, which is why it entered the
and the story is like the Babylonian system and I am counted.

The numbers in this system are numbered and they were made up
from signs of two types: straight wedge for
designation unit
It is marked in tenth century. In s h i l a t from 1 to 59
were written using these signs, as in
USUAL HYPEROGLYPHIC SYSTEM.

In general, I wrote down the axis in positional
The system is counted and based on 60. Let us explain this
on examples.
Therefore, the Babylonian system received
It's called hexadecimal.

To determine the value, the number needed to be
Divide the displayed number into digits on the right
n left. Alternating group of identical signs
("digits") correspondence to alternation
ranks:
= 2 x 6 0 + 12 = 13 2

There was a bad sign, and the role of zero.
It meant the absence of intermediate
discharges. But the absence of junior ranks is not
about symbolized as So, h and word
can mean
and 3 and 18 0 = 3 6 0 and 10 8 0 0 = 3 6 0 6 0 and so on.
It was possible to distinguish such numbers only by the meaning of the word.

The six-decimal system was widely used
in astronomical and chemical calculations up to the era
rebirth. Named use in the 2nd century
AD GREEK MATHEMATICS AND ASTRONOMY CLAUDIUS
P o l e m compiled a table of sinuses
(ancient and ancient times).

Slide 1

Slide 2

Babylonian sexagesimal system Two thousand years BC, in another great civilization - Babylonian - people wrote down numbers differently. Numbers in this number system were made up of two types of signs: Straight wedge (used to denote units) Reclining wedge (to denote tens) The number 60 was denoted by the same sign as 1

Slide 3

Slide 4

1. The number 92 = 60 + 32 was written like this: 2. The number 444 had the form: FOR EXAMPLE: 444 = 7*60 + 24. The number consists of two digits

Slide 5

To determine the absolute value of a number, additional information was required. Subsequently, the Babylonians introduced a special symbol to indicate the missing sixdecimal place, which corresponds in the decimal system to the appearance of the number 0 in the number notation. The number 3632 was written like this: This symbol was usually not placed at the end of the number. The Babylonians never memorized the multiplication tables, because... it was almost impossible to do this. When making calculations, they used ready-made multiplication tables.

Slide 6

The Babylonian sexagesimal system is the first number system known to us based on the positional principle. The Babylonian system played a major role in the development of mathematics and astronomy, and traces of it have survived to this day. So, we still divide an hour into 60 minutes, and a minute into 60 seconds. We divide the circle into 360 parts (degrees).

Slide 7

Slide 8

Table of notation of numbers in Roman numerals Units Tens Hundreds Thousands I 10 X C 1000 M II XX CC 2000 MM 3 III XXX CCC 3000 MMM IV 40 XL 400 CD V 50 L 500 D VI LX 600 DC VII LXX 700 DCC VIII LXXX 800 DCCC 9 IX XC 900 cm

Slide 9

Babylonian number system presentation. Babylonian number system

Material
for the curious

Babylonian number system

Ready-made templates for presentations