1. Mathematical knowledge related to abacus
Abacus.
In ancient times, it was inconvenient for people to use stones to calculate. Later, people switched to using small sticks like chopsticks for calculation, which was called "calculation."
After a period of use, everyone felt that it was too troublesome to use the arithmetic pendulum to perform calculations, so they changed the abacus to a "bead plate" for calculation. Put the beads into the plate to indicate the number to be added, and take out the beads from the plate to indicate the number to be subtracted.
It is the Chinese people who invented the abacus because the beads are easy to roll and scatter when calculating on a bead plate. Threading the beads and arranging them in rows became an abacus. Because calculation with an abacus was fast and convenient, it soon spread to Korea, Japan and other countries.
For more than 1,000 years, abacus has played a positive role in my country's economy, education, culture and other fields, and has spread overseas and has become a testimony of the friendly exchanges and mutual learning between the Chinese people and people around the world. In recent years, scholars in the United States and Japan have hailed abacus as "China's fifth greatest invention."
Transcript of "Dictionary of Anecdotes". .
2. All knowledge or information about the abacus and the invention of the bicycle
Since the invention of the bicycle, it has experienced three changes: The first generation: solid tires, difficult to ride.
Second generation: pneumatic tires, which are easy to break and wear. The third generation: polymer inner tube, no need to inflate, not afraid of puncture, good elasticity, light riding.
Myth 1: The ancestor of the Chinese bicycle was the unicycle in my country more than 500 BC. During the Kangxi period of the Qing Dynasty (1662~1722), Huangluzhuang invented the bicycle.
Volume 11 of "Grand View of Unofficial History of the Qing Dynasty" contains: "A two-wheeled cart made by Huangluzhuang is more than three feet long. It can seat one person. It does not need to be pushed or pulled, and can move on its own. When walking, it is pulled by the hand. Turning around the axle, the bicycle resumes its journey as before, continuing to travel eighty miles."
This is the earliest bicycle in the world. Statement 2: Western Europeans In 1790 AD, the Frenchman Sifulak developed a wooden bicycle without handlebars, pedals, or chains.
The car looks like a wooden horse with two wheels nailed to its feet, and the two wheels are fixed on a line. This car has no driving device or steering device, and the seat cushion is low. When riding on the car, put your feet on the ground and push back hard to make the car move forward in a straight line.
In 1817, Baron von Drais of Germany invented a handlebar that could move freely, making it easier to turn the car. In 1839, K. Macmillan, a British worker, pioneered a pedal bicycle that used a crankshaft mechanism to drive the rear wheel, allowing both feet to leave the ground while riding.
One day in 1861, Parisian carriage and stroller manufacturers Michaud and his son repaired a Delais bicycle and installed a pedal crankshaft on the front wheel of the car, thereby inventing the Michaud bicycle. Soon such bicycles began to be mass-produced. Around 1870, France's Martin made another bicycle with a large driving wheel at the front and a small driven wheel at the back.
After 1890, the British Humber Company produced a chain-driven bicycle with a rhombus shape, which is still in use today. Story 3 Russians One day in September 1801, the Russian serf Artamonov rode a wooden bicycle he made and traveled 2,500 kilometers to Moscow to present a gift to Tsar Alexander I.
The bicycles made by Artamonov are more similar to those made by the Frenchman Sifulak. When Alexander I saw the bicycle made by Artamonov, he immediately ordered the cancellation of his slave status.
The bicycle was invented by Western Europeans. In 1790 AD, the Frenchman Sifulak developed a wooden bicycle without handlebars, pedals, or chains.
The car looks like a wooden horse with two wheels nailed to its feet, and the two wheels are fixed in a line. Since the bicycle had no driving device or steering device and the seat was low, Sifulak rode on the bicycle by himself, put his feet on the ground, and pushed backwards hard to make the bicycle move forward in a straight line.
In 1817, the German Baron von Drais invented a handlebar that could move freely, making it easier to change his bicycle. In 1818, Delais applied for a patent in England.
In 1839, K. Macmillan, a British worker, pioneered a pedal bicycle that used a crankshaft mechanism to drive the rear wheel, allowing people to lift their feet off the ground while riding a bicycle. One day in 1861, Parisian carriage and stroller manufacturers Michaud and his sons were repairing a Delais-style bicycle. After repairing it, when they tried it on a ramp, they found that it was difficult to put their feet on the bicycle, so they improved it. A pedal crankshaft was installed on the front wheel, thus creating the Michaud bicycle, which soon began to be mass-produced.
Around 1870, France's Marcel Merchant made another bicycle with a large driving wheel at the front and a small driven wheel at the back. This kind of bicycle ran better. After 1890, the British Humber Company produced a chain-driven, diamond-shaped bicycle. This type of bicycle is still in use today. The abacus is a calculation tool that everyone is familiar with. The inventor of the abacus is who? What is the exact year of invention? We first saw the word "abacus" from Xu Yue's book "Shu Shu Ji Yi" during the Eastern Han Dynasty.
However, the comments say that it can only do addition and subtraction. Today, it seems that this is at best a prototype of abacus.
Based on the analysis of existing reliable data, abacus was invented in the Song and Yuan Dynasties. Cheng Dawei's book "Zhizhi Algorithm Tongzong" (1592) in the Ming Dynasty was the most widely circulated and influential book dedicated to abacus at that time.
People have consulted a large number of historical documents. From the Song and Yuan Dynasties to the era of Cheng Dawei (1553~1606), they can't find the name of the inventor of the abacus. In fact, the same is true for the calculations mentioned above. This certainly shows that the 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. It is difficult to say where. One person’s work.
Abacus evolved from calculation. Due to the development of society, the requirements for the speed and accuracy of calculations are getting higher and higher, so people have reformed calculations and created a variety of songs.
For example, the motto of 14 7 is "Seven divided by three and advanced into one". Similarly, the motto of 14-7 is "Seven retreats and one returns three" and so on. There is a formula for all addition, subtraction, multiplication and division.
In fact, before the advent of abacus, except for a few division songs, almost all abacus songs were available. After the appearance of the song formula, the calculation speed has increased. If you continue to play with the calculation chips, you will not be able to do what you want.
Many business people who perform calculations outdoors are particularly prone to messing up their calculations and causing errors due to limitations of the objective environment. In this way, it has become an inevitable development trend for abacus to replace calculation. Not only the conditions have been met, but also it has become a very urgent matter.
It was under this circumstance that the craftsmen, calculators and business people at that time worked together to develop an ingenious abacus. The similarities between abacus and calculation are obvious.
Among the numbers represented by abacus chips, one bead on the top is considered five, and one bead on the bottom is considered one. In the abacus, one bead on the top is considered five, and one bead on the bottom is considered one. There is a stipulation in the abacus called "five without a single chip", which means that 5 cannot be represented by just one chip. This is why there are five beads in the middle of the abacus.
Experts in the history of mathematics can also find the basis for the calculation that there are two beads on the middle of the abacus. The above facts are enough to prove that abacus evolved from calculation.
Abacus is one of the major scientific achievements in ancient my country. It has the advantages of simple structure, simple operation, and easy portability, so it is widely used and lasts for a long time.
To this day, abacus is still a compulsory course for primary school students in my country. Although various electronic computers and electronic calculators have become quite popular in the market, their calculations are difficult when doing addition and subtraction.
3. Abacus formula
[5] Abacus formula editor Abacus addition formula Add without carry Add with carry Add straight to five Add to ten Add to break Five to ten Add one: one Up one, down five goes to four, one goes to nine and goes to one plus two: two goes up to two, two goes down to five goes to three, two goes to eight goes to one plus three: three goes up to three, three goes down to five goes to two, three goes to seven and goes to one plus. Four: Four up four, four down five goes to one, four goes to six and goes into one plus five: Five goes up to five, five goes to five and goes into one plus six: Six goes up to six, six goes out to four and goes into one, six goes up and one goes into five and goes into one plus Seven: seven on seven, seven on three, three on one, seven on two, five on one plus eight: eight on eight, eight on two, one on eight, three on eight, five on one plus nine: nine on nine, nine on one. One, nine up, four, five, forward, one. Abacus subtraction formula. Subtraction without abdication. Subtraction in the rebuffed position. Subtraction of five. Subtraction in regressed position. Subtraction of ten. Subtraction of five. Subtraction of one: one down. One up. Four goes to five. One goes back to one. Returns nine minus two: Two down two, two up three goes to five, two goes back one and returns eight minus three: three goes down three, three up two goes back to five, three goes back one and returns seven minus four: four goes down four, four up one goes back to five, four goes back one back Six minus five: Five is five, five is one and five is six. Six is ??six, six is ??one and four is six, six is ??one and five is five. One is minus seven: seven is seven, seven is one and three is seven, seven is one and seven is one. Five goes to two minus eight: eight goes to eight, eight goes back one to return two, eight goes back one to return five, goes to three minus nine: nine goes down to nine, nine goes back one to return one, nine goes back one to return five go back to four, the abacus multiplication formula was used in the Spring and Autumn Period and the Warring States Period It has been used in calculations; the formula for division and division was first seen in Yang Hui's "Multiplication and Division Tongbian Suanbao" [1274], and Zhu Shijie's "Arithmetic Enlightenment" [1299] contains the nine-fold formula, which is basically the same as modern times.
4. How to learn abacus well
Common terms for abacus [edit this paragraph] Gap: When the upper and lower parts of a certain gear are both away from the beam, it is called a gap.
Empty means there is no count in this file, or it means 0. Empty plate: Each position of the abacus is empty, which means that there is no count in the whole abacus, which is called an empty plate.
Inner beads: Counting beads that rely on beams are called inner beads. Outer beads: Liliang's counting beads are called outer beads.
Pulling up: refers to pushing the lower beads against the beam. Pulling down: refers to pushing the upper beads against the beam.
Pulling away: refers to pulling the upper or lower beads away from the beam. This file: refers to the file where you are about to dial the beads to count.
Front gear: refers to the gear before this gear, also called the left gear (bit). Rear gear: refers to the next gear of this gear, also called the right gear (position).
Floating beads: The beads are floating in the middle of the gears because the beads are moved too lightly and do not rest on the beam or frame. Bringing beads: When dialing beads, bringing in or taking out beads that should not be dialed in or out in this or adjacent stalls is called bringing beads in.
Solid beads: Abacus beads that stand against the beam to represent positive numbers. Xu bead: also called negative bead, refers to a hanging bead that is moved so that it neither relies on the beam nor the frame, indicating a negative number.
Number setting: We also teach how to put numbers into the abacus according to the calculation requirements to prepare for calculations. Gear: Also called grade, it refers to the position of the gear.
Wrong gear: Also called misalignment, it means that the beads are not dialed into the correct gear during calculation. Spacer: Also called spacer, it refers to the second space (position) with one space left and right of this number.
When two numbers are multiplied in spaced multiplication, the units digit of the product is placed on the two right digits of the multiplicand; in spaced division, the space quotient refers to the two left digits of the first place of the dividend. . Carry: means that after adding a number to this file, if it is greater than or equal to 10, 1 must be added to the previous digit, which is called carry.
Abdication: It means that when the current gear subtracts a number, the current gear is not enough, and the number in front is reduced by 1, which is called abdication. The first bit: also called the highest bit, refers to the first non-zero digit of a multi-digit number as the first bit.
Such as 3 in 3284, 7 in 0.0726. The last digit: also called the lowest digit, refers to the last number of a multi-digit number.
Such as 5 in 3275, 0 in 120, and 9 in 481.29. Second digit: essentially the second number of a multi-digit number.
Enter 8 in 3865 and 1 in 0.4178. Real numbers: In ancient arithmetic books, multiplicands and dividends are generally called real numbers, or real numbers for short.
Law numbers: In ancient arithmetic books, multipliers and divisors are generally called law numbers, or methods for short.
Multiply and add: means that each digit of the multiplicand is multiplied by each digit of the multiplier, and the product is added while multiplying on the abacus.
Multiplication and subtraction: Also called product subtraction, it means that each quotient is multiplied by the divisor, and the product is subtracted from the dividend. Divisor: refers to the highest digit of the divisor.
The first digit of the product: refers to the first digit of the product number. Quotient: refers to the first digit of the quotient.
Estimating the quotient: In division, if you need to obtain each quotient, you must use mental arithmetic to estimate how many times the dividend is the divisor. This mental arithmetic process is called estimating the quotient. Trial quotient: Also called preliminary quotient, it refers to initially finding a larger or smaller quotient when estimating the quotient, which is called trial quotient.
Set up business: Also called establishing business, it means to put trial business into the abacus. Adjustment of quotient: After placing the quotient, it is proved by multiplication and subtraction that the trial quotient is incorrect and the initial quotient needs to be adjusted.
Confirm the quotient: After setting up the quotient, it is proved by multiplication and subtraction that the trial quotient is neither too big nor too small. Divide to all: It refers to dividing the dividend by the divisor. When dividing to a certain digit, there is no remainder, which is called division to all.
Incomplete division: refers to the indivisible division operation when there is an infinite loop or non-cyclic decimals in the integer division. For example: 1÷3=0.333…; 1÷7=0.142857142857….
Remainder: In a division that cannot be divided into integers, when the quotient reaches each digit or a predetermined certain digit, the number left after subtracting the dividend is called the remainder. During the operation, there is often a remaining number in the product of the dividend and the divisor, which is usually called the remainder.
Withdrawal from business: The initial business was too big, so we changed it to a smaller one and called "withdrawal from business". Supplementary Shang: The initial quotient is too small, so change it to "Supplementary Shang".
False quotient: In the division operation, in order to facilitate calculation, a quotient is first established, and then the correct quotient is obtained through adjustment. The quotient established first is called a fake quotient.
Liquidation: To remove the beads on each beam and make the whole market empty, it is called liquidation. Comprehensive practice: Doing bead-moving exercises on all or most of the abacus gears, as well as comprehensive exercises based on basic operation rules, are called comprehensive exercises.
5. Who knows the abacus formula?
, the addition formula table, add up to five, add to ten, add to break, five to ten, plus one, one, one, one, five, four, one, nine, one Two two up two two down five go three two go eight in one three three up three three down five go two three go seven in one four four up four four down five go one four go six in one five five up five five go five in One six six up, six six up, four in, one six up, one in, five in, 177, up seven, seven in, three in, one seven, two up, five in, 188, up eight eight, two in, one eight, three up, five in, one nine. Nine up nine nine go one in one nine up four go five in one two, the subtraction formula expresses the subtraction of the non-abdication position, the subtraction of the subtracting position without abdication, the subtraction of five, the subtraction of the subtracting position, the subtraction of ten, the complement of five, the subtraction of one, one, one, one, four, go to the five one, retreat one. Also nine two two down two two up three go five two back one back eight three three down three three up two go five three back one back seven four four down four four up one go five four back one back six five five down five five back One back five six six six six back one back four six back one back five go back one seven seven back seven seven back one back three seven back one back five go back two eight eight back eight eight back one back two eight back one back five go back Three-nine-nine, nine-nine, one back, one back, one nine back, one back, five back, four.
6. What is an abacus?
Abacus is also used as a standard.
China is the hometown of the abacus. Today, when computers are widely used, the ancient abacus has not been abandoned. On the contrary, it is still in use in many countries because of its flexibility, accuracy and other advantages. Therefore, people often compare the invention of the abacus with the four great inventions of ancient China.
In the famous Northern Song Dynasty painting "Along the River During Qingming Festival", there is an abacus painted on the cabinet of Zhao Taicheng's medicine shop. Because of the convenience and speed of abacus calculations, it has been a commonly used calculation tool by the Han people for thousands of years. Even the most advanced electronic calculators in modern times cannot completely replace the role of abacus.
The abacus was invented by the Chinese based on their long-term use of arithmetic chips. It was a widely used calculation tool before the advent of digital numbers. Regarding the origin of the abacus, it can be traced back to 600 BC. It is said that our country had an abacus at that time.
The ancients strung ten beads into a group, arranged the groups, put them into the frame, and then quickly moved the beads to perform calculations. In ancient times, people used small wooden sticks to perform calculations. These small wooden sticks were called abacus, and calculations using abacus as a tool were called abacus.
Later, with the development of production, calculations using small wooden sticks were restricted, so people invented a more advanced calculation tool-the abacus. By the Ming Dynasty, abacus could not only perform addition, subtraction, multiplication and division operations, but also calculate land area and the size of various shapes.