bead arithmetic
In ancient times, it was inconvenient for people to calculate with stones. Later, people used sticks such as chopsticks to calculate, which was called "calculation".
After a period of use, everyone thought it was too much trouble to calculate with the calculation pendulum, so they changed the calculation to "bead plate" to calculate. Put the beads on the plate to indicate the number to be added, and take out the beads on the plate to indicate the number to be subtracted.
It was our people who invented abacus, and when calculating with a bead plate, the beads rolled away easily. Putting the beads on and arranging them became an abacus, because it was fast and convenient to calculate with an abacus, and it soon spread to South Korea, Japan and other countries.
/kloc-since 0/000, abacus calculation has played an active role in China's economy, education, culture and other fields, and spread overseas, which has become a witness of friendly exchanges and mutual learning between the people of China and people of other countries. In recent years, American and Japanese scholars praised the abacus as "the fifth invention of China".
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2. All knowledge or information about the invention of abacus and bicycle
Bicycles have undergone three changes since their invention: the first generation: solid tires, which are difficult to run.
The second generation: pneumatic tires, easy to break and wear. The third generation: polymer inner tube, no inflation, no fear of pricking, good elasticity and light riding.
Statement 1: The ancestor of bicycles in China was China's unicycle over 500 BC. During the Kangxi period of Qing Dynasty (1662~ 1722), Huang Lvzhuang once invented bicycles.
"Grand View of unofficial history in Qing Dynasty" has been published for eleven years: "Huang Lvzhuang built a two-wheeled vehicle, which is more than three feet long and can sit for one person without pushing or pulling. When walking, turn your arm around the axis, then walk as before, and walk 80 miles around the sun with your arm. "
This is the earliest bicycle in the world. Statement 2: In A.D. 1790, the Western Europeans developed a wooden bicycle without handlebars, pedals and chains.
This car looks like a wooden horse, with two wheels nailed to its feet and fixed on a line. This car has no driving device and steering device, and its seat cushion is low. When riding a car, put your feet on the ground and push back hard to make the car go straight ahead.
18 17, the German baron von delaisse invented a handlebar that can move freely, making it easier to change cars. 1839, K. Macmillan, a British worker, pioneered a pedal bicycle with a crankshaft mechanism to drive the rear wheels, so that both feet can leave the ground when riding.
186 1 year, Messau and his son, a Parisian carriage and stroller manufacturer, repaired the delaisse bicycle and installed a pedal crankshaft on the front wheel of the car, thus inventing the Michaud bicycle, and soon began mass production. Around 1870, a Frenchman, Ma Zhi, made a bicycle with a big front driving wheel and a small rear driven wheel.
1890, Humber Company of England produced a diamond bicycle with chain drive, which has been in use ever since. Statement III One day in September, Artamonov, a Russian serf, rode his wooden bicycle and traveled 2,500 kilometers to Moscow to present a gift to Tsar Alexander I.
Bicycles produced in Artamonov are similar to those produced in Sifrak. When Alexander I saw the bicycle made by Artamonov, he immediately ordered the abolition of his slave status.
Bicycles were invented by western Europeans. In A.D. 1790, the Frenchman Sifrak developed a wooden bicycle without handlebars, pedals and chains.
The car is shaped like a wooden horse, with two wheels nailed to its feet and fixed on a line. Because this bicycle has no driving device and steering device, and the seat cushion is low, Sifrak rides on the bicycle by himself, with his feet on the ground and pushing back hard to make the bicycle move straight forward.
18 17, the German baron von delaisse invented a handlebar that can move freely, making his bicycle easier to replace. Delaisse applied for a patent in Britain.
1839, K. Macmillan, a British worker, pioneered a pedal bicycle with a crankshaft mechanism to drive the rear wheels, so that people can leave their feet off the ground when riding a bicycle. 186 1 year, one day, Michelson, a Parisian carriage and stroller manufacturer, repaired delaisse's bicycle. After the repair, they found it difficult to put their feet on the ramp, so they improved it, and installed a pedal crankshaft on the front wheel of the car, thus inventing Michelle's bicycle, which soon began mass production.
Around 1870, a Frenchman, Ma Zhi, made a bicycle with a big front driving wheel and a small rear driven wheel. This kind of bike runs well. 1890, Humber Company of England produced a chain-driven diamond-shaped bicycle. This kind of bicycle has been in use ever since. Abacus is a familiar computing tool. Who is the inventor of abacus? What is the exact year of invention? We first saw the word "abacus" in Xu Yue's book Numerology Legacy in the Eastern Han Dynasty.
However, the note says that only addition and subtraction can be done. Today, it seems that this theory is the embryonic form of an abacus.
From the analysis of available reliable data, abacus was invented in Song and Yuan Dynasties. Cheng Dawei's "Directing at Arithmetic, Unifying Clan" (1592) in Ming Dynasty is the most widely circulated and influential book on abacus calculation.
People have consulted a large number of historical documents, and from the Song and Yuan Dynasties to the Cheng Dawei era (1553~ 1606), they can't find the name of the inventor of the abacus. In fact, the same is true of the above calculation and financing. On the one hand, it shows that feudal rulers did not pay enough attention to scientific and technological inventions, on the other hand, it also shows that their inventions are a gradual process, which is gradually improved and perfected, and it is difficult to say which party is responsible.
The abacus evolved from calculation. Due to the development of society, the speed and accuracy of calculation are increasingly demanding, so people have reformed the calculation and created various songs.
For example, the melody of 14+7 is "seven divided by three is one". Similarly, the melody of 14-7 is "seven retreats, one returns three" and so on. All addition, subtraction, multiplication and division have a set of songs.
In fact, before the abacus appeared, almost all the abacus rhymes were ready except for a few division rhymes. After the appearance of rhyme, the calculation speed has increased, and it will be overwhelming to continue to fool around with calculation.
Due to the limitation of the objective environment, many business people who do calculations outdoors are particularly prone to make mistakes. In this way, abacus instead of calculation has become an inevitable development trend, not only the conditions have been met, but also a very urgent matter.
It was in this situation that craftsmen, calculators and businessmen at that time worked together to develop a sophisticated abacus. The similarity between abacus and calculation is obvious.
Among the calculated figures, one is raised to five and the other is raised to one; In the abacus plate, one bead in the file is five, and the next bead is one. There is an agreement in the calculation called "five", which means that five can't be represented by a single chip, which is why there are five beads in the middle of the abacus.
Experts in the history of mathematics can also find the calculation basis that there are two beads in the middle of the abacus. The above facts are enough to prove that the abacus evolved from calculation.
The abacus is one of China's great scientific achievements in ancient times. It has the advantages of simple structure, simple operation and convenient carrying, so it is widely used and lasts for a long time.
Until today, abacus calculation is still a compulsory course for primary school students in China. Although all kinds of electronic computers and calculators are quite popular in the market, their calculation is very difficult when adding and subtracting.
3. Abacus formula
[5] Abacus formula editing Abacus formula addition without carry plus shun plus all five plus ten plus break five into ten plus one: one up one, one down five to four, one to nine into one plus two: two up two, two down five to three, two to eight into one plus three: three up three, three to five to two, three to seven into one plus four: four up four, four down five to one, four to six into one plus five. Seven to three into one, seven to two to five into one plus eight: eight to eight, eight to two into one, eight to three to five into one plus nine: nine to nine, nine to one into one, nine to four to five into one, abacus subtraction formula, no abdication, demotion, direct reduction, reduction of five, reduction of ten to five, reduction of one to one, reduction of one to nine, reduction of two to two. Four retreats, one return, six minus five: five retreats, one return, five minus six: six retreats, one return, one return, one subtract seven: seven retreats, one return, three return, seven retreat, five return, two subtract eight: eight retreat, one return, five return, three subtract nine: nine retreat, nine retreat, one return, five return, four abacus. For the formula of "returning to nine", see Yang Hui's "Calculating Treasure by Multiplication" [1274] and Zhu Shijie's "Arithmetic Enlightenment" [1299], and the formula of "returning to nine" is basically the same as that of modern times.
4. How to learn abacus well
Notch: When the upper and lower parts of a certain file are separated from the beam, it is called a notch.
Neutral means this gear doesn't count, or it means 0. Empty disk: All gears of the abacus are in neutral, that is to say, there is no counting at all. This is called empty disk.
Inner beads: The counting beads counted by the light beam are called inner beads. Outer beads: Counting beads that are not counted from the light beam are called outer beads.
Pull up: refers to pulling up the lower bead against the beam. Pull: refers to pulling the upper bead towards the beam.
Pull out: refers to pulling the upper bead or the lower bead away from the beam. This file: it is the file that corrects the number of strokes.
Previous gear: refers to the previous gear of this gear, also called left gear (bit). Rear gear: refers to the rear gear of this gear, also called right gear (position).
Floating beads: the force is too light when pulling the beads, and the beads float in the middle of the file. With beads: when pulling beads, call with beads to bring in or out the beads that should not be pulled in or out of this file or adjacent files.
Real beads: Beads that represent positive numbers with light beams. Virtual bead: Also known as negative bead, it refers to a suspended bead that is not set as a beam or a border, indicating a negative number.
Set the number: also teach the number, according to the calculation requirements, dial the number into the abacus and prepare for calculation. Gear: also called grade, it refers to the grade of gear.
Wrong gear: also known as dislocation, it means that the abacus does not dial the gear it should dial during the operation. Shift: Also called shift, it refers to the second gear (position) of one gear left and right of this digit.
In cross multiplication, two numbers are multiplied, and the number of digits of the product is played on the right two digits of the multiplicand; In each division, each quotient refers to the left two digits of the first dividend. Carry: it means that this file is greater than or equal to 10 after adding a number, and the previous position must be added with 1, which is called carry.
Abdication: it means that when a number is subtracted from this file, the file is not enough, and the previous 1 is allowed to be subtracted, which is called abdication. First digit: Also called the highest digit, it means that the first non-zero digit of a multi-digit is the first digit.
Such as 3 in 3284 and 7 in 0.0726. Last digit: Also called the lowest digit, it refers to the last digit of a multi-digit number.
For example, 0.4865438 in 5,120+9 in 3275. Second digit: The second digit of a multi-digit number.
Enter 8,0.465438 in 3865 and 1 in 078. Real number: Multiplier and dividend are generally called real numbers in ancient arithmetic books.
Normal number: Multiplier and divisor are commonly known as normal numbers in ancient books, which is abbreviated as law. Multiplication and addition: refers to multiplying each bit of the multiplicand by each bit of the multiplier, and adding the products while multiplying in abacus.
Multiplication and subtraction: Also called subtraction product, it means that each quotient is multiplied by the divisor, and the divisor subtracts the product. Prefix: refers to the highest digit of divisor.
Product header: refers to the first digit of the product. Quotient: refers to the first digit of quotient.
Quotient estimation: in division, everyone who requires it must calculate carefully, and the dividend estimation is several times that of the divisor. This mental arithmetic process is called quotient estimation. Trial quotient: also known as initial quotient, refers to the initial quotient obtained when estimating quotient, which is called trial quotient.
Buyer: Also known as establishing a business, it refers to putting the trial business in the abacus. Quotient adjustment: after releasing the quotient, multiplication and subtraction are used to prove that the trial quotient is incorrect, and the initial quotient needs to be adjusted.
Positive quotient: after putting the quotient, prove that the quotient is neither too big nor too small by multiplication and subtraction. Division: Divide the dividend by the divisor, and divide it to a certain bit, and there is just no remainder. This is called division.
Infinite divisor: refers to the number that cannot be divided when there is infinite cycle or acyclic decimal. Such as:1÷ 3 = 0.333 ...; 1÷7=0. 142857 142857……。
Remainder: division that is not divisible. When the quotient reaches each number or a predetermined number, the remaining number in the dividend is called the remainder. In the process of operation, there is always a remainder in every product of the quotient and divisor in the suburb of dividend, which is usually called remainder.
Withdrawal of business: the initial business is too big, so it is changed to "Withdrawal of business". Supplementary business: the initial business is too small, so it is called "supplementary business".
Pseudo-quotient: In the division operation, for the convenience of calculation, a quotient is established first, and then the exact quotient is obtained after adjustment. The first definite quotient is called false quotient.
Liquidation: remove the beads from each booth and leave the whole booth vacant. This is called liquidation. Overall practice: All abacus files, or most files, are used for pinball practice, and comprehensive practice is carried out according to the basic algorithm, which is called overall practice.
5. Who knows the abacus formula?
The addition formula table directly adds five to ten plus five plus ten plus one, one, five, four, one, nine, one, two, two, five, three, two, eight, one, three, three, five, four, four, six, one, five, five, one, six, four.
6. What is an abacus
Abacus, also called dial.
China is the hometown of abacus. Today, computers have been widely used. The ancient abacus has not been abandoned, but it is in the ascendant in many countries because of its convenience and accuracy. Therefore, people often compare the invention of abacus with four great inventions of ancient china.
In the famous painting The Riverside Scene at Qingming Festival in the Northern Song Dynasty, an abacus was painted on the cabinet of Zhao Taicheng's drugstore. Because of its convenient operation, abacus has been widely used by the Han people for thousands of years, and even the most advanced modern electronic calculator can not completely replace the role of abacus.
The abacus was invented by China people on the basis of long-term use of calculation funds, and it was a widely used calculation tool before the appearance of * * * numbers. The origin of abacus can be traced back to 600 BC. It is said that there was a computing board in China at that time.
The ancients strung ten abacus beads into a group, arranged them in groups, put them in a box, and then quickly set aside the abacus beads for calculation. In ancient times, people used small sticks to calculate. These sticks are called computing chips, and calculations with computing chips as tools are called computing chips.
Later, with the development of production, the calculation with sticks was restricted, so people invented a more advanced calculation tool-abacus. By the Ming Dynasty, abacus could not only add, subtract, multiply and divide, but also calculate the land area and the size of things of various shapes.