Throughout his life, every man is always something to learn, and the knowledge gained after a certain time seem so natural, that are perceived as a familiar fact.The head is not even the thought creeps in: how it all began?As people learned to count and tell time?How long society has come to realize that the world is subject to almost all the numbers?
As people learned to take the time
It is in the modern world 365 days a year, 30 days in a month and 24 hours in a day are a natural fact.In the past, when there was no knowledge of the amount of time a person was satisfied with the methods invented by yourself and tool for this is the sun.On any surface installed dial with markers and six, the shadow of which move in a circle.Depending on weather conditions is a significant drawback of such a device: the overcast sky and the rain made it impossible to determine the time.The analogue of such a structure in the world today are the clock firmly gained its niche and become an indispensable item in a person's life.
The timing of the stars, water and fire
stars - symbol of romance and dreams of something distant and beautiful, served as a kind of determinant of time during the night.For this was invented star charts, the measurement of which took place with the help of the transit instrument.
addition to stellar and solar clock, popular in almost all nations, and differ only in design, relatively large quantities of water used in the exhibits, which are cylindrical tank, from which water flowed drop by drop.That's the number of people metered water dripped-off time.These watches have been popular in Egypt, Rome, Babylon.A man learned to take the time in Asia?Here, in devices such as the water used by the reverse principle: floating vessel filled with water flowing through a small hole.
trying to bring into your life, not only water, but also the element of fire, and a man came up fire watch, who took their origin in China and won with time the popularity throughout Europe.The basis for these devices determines the time is a combustible material (in the form of a stick or coil) and attached metal balls, falling at a certain proportion the combustion material.In Europe, mainly used candle clock, preferring their lamp-and wicking.Time it determines the amount of burnt wax.Especially prevalent these watches were in churches and monasteries.
Hourglass - the pride of modern rarity
Of course, the most popular were the hourglass, which is being actively used to perform its basic functions, as well as decorative items.Accuracy computable time in devices of this type depends on the quality sand, it determines the uniformity of flowability.
History of Science counting
Understanding time in its quantitative indicators are the determining factor for learning numbers and numeracy.And the history of the origin account for so long that looks more like a fairy tale.As people learned to count?Many centuries ago, mankind lived tribes led a gregarious lifestyle, to dress in the skins of dead animals and feed on the fact that its representatives could get themselves.
Accordingly, improvised tools for survival and foraging are the simplest tools: sticks and stones.Perhaps the constant dangers and the need for food production became the main impetus to the need to account, which in our time is not only perceived as a natural fact, but also facilitated with the help of modern computer technology.
One, two, and many
first concept that refers to the number and explain how people have learned to count, were "one" and "many.""One" - separately allocated according to certain criteria or individual object: leader of the pack, grain in the ear, etc."Many" - the total mass, in which the subject is.
The emergence of "two", meaning "couple": the eyes, ears, paws, wings, hand, explains how people learned to count in times of non-existent numbers.Talking about the two ducks caught, the hunter was pointing to his eyes, explaining thus the amount of trophies.
In counting the science of the ancient world there was gradual progress: were already known number "one", "two" and "many."Soon, a man came to what became of the total weight of the allocated three, four, five or more subjects, and this number had no name, and explained how the amount known at the time the numbers "2" and "1".For example, "3" - a "1" and "2" in total;"4" - the amount of "2" and "2";and "5" - "2", "2" and "1" together.In Tibet, the number "2" is the wings in India - eyes, some people "1" - is the moon, "5" - the hand.That is, each number was first visually-associative perception before getting title.
Account as a vital necessity
As people have learned to believe that if the ability of "art" in every stage of human development becomes necessary?While hunting in the surroundings of the beast elder hunter wanted the right to assign people to take an animal in the ring.For this, he showed on his fingers, where and how many people need to take the desired position ..
in trade to indicate the price was also applied mathematics fingers (and toes if the cost was high).For example, the exchange made spears into the skins of animals, the seller put his hand on the ground and showed that in front of each finger is required to put a skin.By the way, the folding finger denotes the addition, and their extension - subtraction.It was the first mathematical examples explaining how the ancient people learned to count in the distant past.
Accounts science in different countries
Many countries have retained in its history, a model of how people have learned to count, still using the legacy of the past: in Japan and China household use is considered fives and tens;in England and France - twenties.
As people learned to count?Where did the numbers and numbers?The first way of writing numbers were notches on trees and tying knots on the ropes.
ancient Egyptians, depicting any action in the form of pictures on papyrus, as those numbers are not recorded.The inhabitants of ancient Rome number indicates dashes.So «I» - this is one, «V» - the image brush protruding toward the finger, or rather five fingers in a simplified form, an "X" - two five fingers put together.
With the advent of letters for numbers began to use alphabet.For example: B
With the advent of letters for numbers began to use alphabet.For example: C - is "2" D - "3" D - "4" E - "5".To distinguish the letters and numbers over the last raised the icon called "Titley."The method was not very comfortable, since it is not allowed to write large numbers.Over time, people began to separate from the number of letters and taken alone, regardless of the subject.
Modern Arabic numerals, which are widely used everywhere today, was invented in India, and in our country have been applied in the 18th century.Do not lose popularity and Roman numbers on the date appearing on the watch dial, and used to identify the centuries and chapters in books.
Distinguished way bills Ancient Babylon, where for 6000 years BC already was conducted mathematical records of business transactions.Entries of this kind depicted images (characters) in the form of narrow horizontal and vertical wedges, hence the name "cuneiform".
Unit designated one wedge, deuce - two and so on.The number "10" allocated broad wedge and had a special name.His flourishing mathematics Babylon experienced during the reign of King Hammurabi.In written sources of that time period we found evidence of how people learned to write and read long before our times.This recording complex computing operations, as well as solving quadratic and cubic equations.
How to learn to count in your mind
If such complex operations were under the power of our ancestors, the modern generation of mathematics through an enhanced time and a lot of great minds, should not be particularly difficult.However, the availability of computers, the ability to produce digital action instead of a man greatly facilitates mental work of the latter.Therefore, an oral account, helping to develop and train memory skills should own each.Learning this kind of mental activity will be successful if there are:
- capacity, which together with the mental concentration to help focus on the task at hand and keep in mind the complex numbers;
- knowledge of formulas that lead to easy made computing operations;
- practice that, along with regular training allows us to develop and improve skills.
Examples of simple mental accounts
add, subtract, multiply and divide numbers without making any entries on paper or using calculators is a snap.Here are a few examples of how to learn to count in your mind without much difficulty:
Multiply by 4
Easy way in which the number must be multiplied by 2 and the result is once again doubled.For example:
4 = 35 * 35 * 2 = 70 * 2 = 140
Multiply by 11
figures two-digit number, multiplied by 11, as it is required to push.
48 * 11 = 4, and 8 * 11
then folded required number of digits, in this case 4 and 8, and the result will be a response.Important to remember that if the summation result is a two-digit number, then only need to leave the unit, and add to the tens 1.
4 (12) 8 = 5 2 8 = 528. That is the result of 12 units left - a 2,and added to the top ten 1.
to this action did not cause any difficulties, need to increase the number twice and move one digit comma ago.
125/5 = 125 * 2 = 250 (offset point) = 25
In this case, the pattern is similar: the number is multiplied by 2 and divided by 100.
600/50 =600 * 2/100 = 12
number multiplied by four and divided by 100.
700/25 = 700 * 4/100 = 28
Addition and subtraction of natural numbers
At addition of natural numbers should beknow a trick that if one of the terms to increase by a certain number (in order to facilitate the account), the same number must be subtracted from the result.
787 + 193 = (787 + 193+ 7 (to round 193 to 200)) - = 7 (787 200) - 7 = 980