Little knowledge of mathematics 1. Know little about mathematics

1, as early as more than 2000 years ago, our ancestors used magnets to make an instrument to indicate the direction. This instrument is Sina.

2. German mathematician kravis was the first to use points as decimal points.

"Tangram" is a jigsaw puzzle in ancient China. It consists of seven thin plates, which can be put together into a big square. The patterns spelled out are varied, and later spread abroad, called Tang Tu.

It is said that as early as 4500 years ago, our ancestors used notch to measure time.

6. China is the first country to use the rounding method.

7. Euclid's most famous work, The Elements of Geometry, is the foundation of European mathematics. It put forward five postulates and developed them into Euclidean geometry, which is widely regarded as the most successful textbook in history.

8. Zu Chongzhi, a mathematician, astronomer and physicist in the Southern Dynasties, ranked the value of pi in the seventh place.

9. Rudolph, a Dutch mathematician, calculated the 35th place of pi.

10 Archimedes, known as the "father of mechanics", has many mathematical works handed down from generation to generation. Archimedes once said: Give me a fulcrum and I can move the earth. This sentence tells us that we should have the courage to find this fulcrum and use it to find the truth.

Extended data

Mathematics (Mathematics or maths, from the Greek word "Má thē ma"; Often abbreviated as "mathematics"), it is a discipline that studies concepts such as quantity, structure, change, space and information, and belongs to a formal science from a certain point of view.

In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.

Resource Mathematics _ Sogou Encyclopedia

2. A little knowledge about mathematics

1, zero

At a very early time, people thought that "1" was the beginning of "numerical character table", which further led to other numbers such as 2, 3, 4 and 5. The function of these figures is to count those physical objects, such as apples, bananas and pears. Only later, when there were no apples in the box, did I learn how to count the apples in the box.

2. Digital system

Digital system is a way to deal with "how much". Different cultures have adopted different methods in different times, from the basic "1, 2,3, many" to the highly complex decimal notation used today.

3,π

π is the most famous number in mathematics. Forget all other constants in nature, and you won't forget them. π always appears at the first place in the list. If the number also has an Oscar, then π will definitely win the prize every year.

π or π is the ratio of the circumference of a circle to its diameter. Its value, that is, the ratio of these two lengths, does not depend on the size of the circumference. Whether the circumference is large or small, the value of π is constant. π comes from the circumference, but it is everywhere in mathematics, even involving those places that have nothing to do with the circumference.

4. Algebra

Algebra gives a brand-new method of solving problems, a "cyclotron" method of playing with years. This kind of "maneuver" is "reverse thinking". Let's consider this problem. When the number 25 is added with 17, the result is 42. This is a positive idea. All you need to do is add up these figures.

However, if you already know the answer 42 and ask a different question, what you want to know now is what number and 25 add up to 42. You need to use reverse thinking here. To know the value of unknown x, satisfy equation 25+x=42, and then subtract 25 from 42 to know the answer.

5. Function

Leonhard euler is a Swiss mathematician and physicist. Euler was the first person to use the word "function" to describe expressions containing various parameters, such as: y? =? F(x), one of the pioneers who applied calculus to physics.

3. A little knowledge about mathematics

Yang Hui Triangle is a triangular numerical table arranged by numbers, and its general form is as follows:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 2 1 35 35 2 1 7 1

… … … … …

The most essential feature of Yang Hui Triangle is that its two hypotenuses are all composed of the number 1, and the other numbers are equal to the sum of the two numbers on its shoulders. In fact, ancient mathematicians in China were far ahead in many important mathematical fields. The history of ancient mathematics in China once had its own glorious chapter, and the discovery of Yang Hui's triangle was a wonderful one. Yang Hui was born in Hangzhou in the Northern Song Dynasty. In his book "Detailed Explanation of Algorithms in Nine Chapters" written by 126 1, he compiled a triangle table as shown above, which is called an "open root" diagram. And such triangles are often used in our Olympic Games. The simplest thing is to ask you to find a way. Now we are required to output such a table through programming.

At the same time, this is also the law of quadratic coefficient of each term after polynomial (A+B) n is opened, that is

0(a+b)^0 0 NCR 0)

1(a+b)^ 1 1 NCR 0)( 1 NCR 1)

2(a+b)^2(2 NCR 0)(2 NCR 1)(2 NCR 2)

3 votes (A+B) 3 (3 abstentions) (3 abstentions 1) (3 abstentions and 2 abstentions) (3 abstentions and 3 abstentions)

. . . . . .

Therefore, the Y term of X layer of Yang Hui triangle is directly (y nCr x).

It is not difficult for us to get that the sum of all terms in layer X is 2 x (that is, when both A and B in (A+B) x are 1).

[the above y x refers to the x power of y; (a nCr b) refers to the number of combinations]

In fact, ancient mathematicians in China were far ahead in many important mathematical fields. The history of ancient mathematics in China once had its own glorious chapter, and the discovery of Yang Hui's triangle was a wonderful one.

Yang Hui was born in Hangzhou in the Northern Song Dynasty. In his book "Detailed Explanation of Algorithms in Nine Chapters" written by 126 1, he compiled a triangle table as shown above, which is called an "open root" diagram.

And such triangles are often used in our Olympic Games. The simplest thing is to ask you to find a way. Specific usage will be taught in the teaching content.

In foreign countries, this is also called Pascal Triangle.

4. Know little about mathematics

The origin of mathematical symbols

Besides counting, mathematics needs a set of mathematical symbols to express the relationship between number and number, number and shape. The invention and use of mathematical symbols are later than numbers, but they are much more numerous. Now there are more than 200 kinds in common use, and there are more than 20 kinds in junior high school math books. They all had an interesting experience.

For example, there used to be several kinds of plus signs, but now the "+"sign is widely used.

+comes from the Latin "et" (meaning "and"). /kloc-in the 6th century, the Italian scientist Nicolo Tartaglia used the initial letter of "più" (meaning "add") to indicate adding, and the grass was "μ" and finally became "+".

The number "-"evolved from the Latin word "minus" (meaning "minus"), abbreviated as m, and then omitted the letter, it became "-".

/kloc-In the 5th century, German mathematician Wei Demei officially determined that "+"was used as a plus sign and "-"was used as a minus sign.

Multipliers have been used for more than a dozen times, and now they are commonly used in two ways. One is "*", which was first proposed by the British mathematician Authaute at 163 1; One is "",which was first created by British mathematician heriott. Leibniz, a German mathematician, thinks that "*" is very similar to Latin letter "X", so he opposes the use of "*". He himself proposed to use "п" to represent multiplication. But this symbol is now applied to the theory of * * *.

/kloc-In the 8th century, American mathematician Audrey decided to use "*" as the multiplication symbol. He thinks "*" is an oblique "+",which is another symbol of increase.

""was originally used as a minus sign and has been popular in continental Europe for a long time. Until 163 1 year, the British mathematician Orkut used ":"to represent division or ratio, while others used "-"(except lines) to represent division. Later, in his book Algebra, the Swiss mathematician Laha officially used "∫" as a division symbol according to the creation of the masses.

/kloc-in the 6th century, the French mathematician Viette used "=" to indicate the difference between two quantities. However, Calder, a professor of mathematics and rhetoric at Oxford University in the United Kingdom, thinks that it is most appropriate to use two parallel and equal straight lines to indicate that two numbers are equal, so the symbol "=" has been used since 1540.

159 1 year, the French mathematician Veda used this symbol extensively in Spirit, and it was gradually accepted by people. /kloc-In the 7th century, Leibniz in Germany widely used the symbol "=", and he also used "∽" to indicate similarity and ""to indicate congruence in geometry.

Greater than sign ">" and less than sign "

The origin and early development of mathematics;

Mathematics, like other branches of science, is an intellectual accumulation developed through human social practice and production activities under certain social conditions. Its main content reflects the quantitative relationship and spatial form of the real world, as well as their relationship and structure. This can be confirmed from the origin of mathematics.

The Nile in ancient Africa, the Tigris and Euphrates rivers in West Asia, the Indus and Ganges rivers in Central and South Asia, and the Yellow and Yangtze rivers in East Asia are the birthplaces of mathematics. Due to the need of agricultural production, the ancestors in these areas have accumulated rich experience from long-term practical activities such as irrigation, measuring field area, calculating warehouse volume, calculating calendars suitable for agricultural production, and related wealth calculation and product exchange, and gradually formed corresponding technical knowledge and related mathematical knowledge.

5. Give some math stories and knowledge. Be brief.

One day, the Tang Priest told his disciples Wukong, Bajie and Friar Sand to go to Huaguoshan to pick peaches. Soon, the three disciples came back happily after picking peaches. Tang Priest and his disciples asked: How many peaches did each of you pick? Bajie said with a silly smile, Master, let me test you. Each of us took the same amount of money. There are less than 65,438+000 peaches in my basket. If you count three plots, there is still 1 left. Do you calculate how many peaches each of us picked? Friar Sand said mysteriously, Master, I will test you, too. If there are four peaches in my basket, there is 1 left in the end. Calculate, how many peaches did we each pick? Wukong smiled and said, Master, I'll test you, too. If you count five peaches in my basket, there is 1 left in the end. Calculate, how much will each of us choose? 2 Digital Fun Association Su Dongpo, a great poet in the Song Dynasty, went to Beijing with several schoolmates to take the exam when he was young. When they arrived at the examination center, it was too late. The examiner said, "I made an association. If you are right, I will let you into the examination room." The examiner's first association is: a single leaf in a boat, two or three students, four oars and five sails, passing through six beaches and seven bays, but it's too late. Su Dongpo has been tested three times and twice, and I must get a correct answer today. Examiners and Su Dongpo both embedded ten numbers from one to ten in couplets, which vividly described the hardships and assiduousness of literati. Learning mathematics with three wrong decimal points not only requires correct thinking, but also can't make mistakes in the specific problem-solving process. An old woman living on a pension in Chicago, USA, went home after a minor operation in the hospital. Two weeks later, she received a bill from the hospital for $63,440. When she saw such a huge number, she couldn't help being surprised. She had a heart attack and fell to the ground dead. Later, someone checked with the hospital, and it turned out that the computer misplaced the decimal point, but in fact she only had to pay $63.44. A wrong decimal point actually killed a person. As Newton said, "in mathematics, even the smallest error can't be made."

6. Little knowledge after math class

Mathematical knowledge "The Elements of Geometry" is the immortal work of Euclid, an ancient Greek mathematician. It is the crystallization of the achievements, methods, thoughts and spirit of the whole Greek mathematics at that time. Its content and form have great influence on geometry itself and the development of mathematical logic. Since its publication, it has been popular for more than 2000 years. It has been translated and revised many times. Since 1482 was first printed and published, there have been more than 000 different versions of 1000. Apart from the Bible, there are no other works, and its research, use and dissemination can be compared with the Elements of Geometry. However, the Elements of Geometry has transcended the influence of nationality, race, religious belief and cultural consciousness, but it is the Bible that has made it. Accumulated a wealth of material. Greek scholars began to organize the mathematical knowledge at that time in a planned way and tried to form a strict knowledge system. The first attempt in this respect was Hippocrates in the 5th century BC, which was later revised and supplemented by many mathematicians. By the 4th century BC, Greek scholars had laid a solid foundation for building a theoretical building of mathematics. On the basis of predecessors' work, Euclid collected and sorted out the rich mathematical achievements of Greece, restated them in the form of propositions, and strictly proved some conclusions. His greatest contribution is to select a series of meaningful and primitive definitions and axioms, arrange them in strict logical order, and then deduce and prove them on this basis. The Elements of Geometry with axiomatic structure and strict logic system has been formed. The Greek edition of Elements of Geometry has been lost, and all modern editions are based on the revised edition written by Greek critic Theon (about 700 years later than Euclid). The revised volume of Elements of Geometry is 13, with 465 propositions. Its content is to expound the systematic knowledge of plane geometry, solid geometry and arithmetic theory. In the first volume, some necessary basic definitions, explanations, postulates and axioms are given, including some well-known theorems about congruence, parallel lines and straight lines. The last two propositions in this volume are Pythagoras theorem and its inverse theorem. Here we think of a short story about the English philosopher T. Hobbes: One day, Hobbes happened to be reading Euclid's Elements of Geometry. It is out of the question. "He carefully read the proof of each proposition in the first chapter from back to front until he was completely convinced by axioms and postulates. The second volume is not long This paper mainly discusses the geometric algebra of Pythagoras school. The third volume includes some famous theorems of circle, chord, secant, tangent, central angle and circumferential angle. Most of these theorems can be found in the current middle school mathematics textbooks. The fourth volume discusses the ruler drawing of some inscribed and circumscribed regular polygons of a given circle. The fifth volume gives a wonderful explanation of eudoxus's proportional theory, which is considered as one of the most important mathematical masterpieces. Porzano (Porzano, 178 1- 1848), an unknown mathematician and priest in Czechoslovakia, happened to be ill while vacationing in Prague. In order to distract him, he picked up the Elements of Geometry and read the fifth volume. He said that this ingenious method made him excited and completely relieved his illness. He always recommends it as a panacea to patients. In the seventh, eighth and ninth volumes, elementary number theory is discussed, Euclid algorithm for finding the greatest common factor of two or more integers is given, proportion and geometric series are discussed, and many important theorems about number theory are given. The tenth volume discusses unreasonable quantities, that is, incommensurable line segments, which are difficult to read. The last three volumes are the eleventh, twelfth and twelfth volumes. This paper discusses solid geometry. At present, most of the contents in middle school geometry textbooks can be found in Geometry Elements. According to the axiomatic structure and using Aristotle's logical method, Geometry Elements established the first complete knowledge system of geometric deduction. The so-called axiomatic structure is to select a small number of unproven original concepts and propositions as definitions, postulates and axioms, making them the starting point and logical basis of the whole system. Then use logical reasoning to prove other propositions. For more than 2000 years, The Elements of Geometry has become an excellent example of using axiomatic methods. Admittedly, as some modern mathematicians have pointed out, The Elements of Geometry has some structural defects. But this does not detract from the lofty value of this work. Its far-reaching influence makes "Euclid" and "geometry" almost synonymous. It embodies the mathematical thought and spirit laid by Greek mathematics and is a treasure in human cultural heritage. Goldbach conjecture Goldbach conjecture 1742 Goldbach in Germany wrote a letter to Euler, a great mathematician living in Petersburg, Russia, in which he raised two questions. Such as 6 = 3+3, 14 = 3+ 1 1 and so on. Second, can every odd number greater than 7 represent the sum of three odd prime numbers? Such as 9=3+3+3, 15=3+5+7, etc. This is the famous Goldbach conjecture. This is a famous problem in number theory, which is often called the jewel in the crown of mathematics. In fact, the correct solution of the first question can lead to the correct solution of the second question, because every odd number greater than 7 can obviously be expressed as an even number greater than 4 and 3.50010.00000001005. The Soviet mathematician vinogradov proved that every odd number large enough can be expressed as the sum of three odd prime numbers with his original "triangular sum" method, which basically solved the second question. But the first problem has not been solved. Because the problem is too difficult, mathematicians began to study the weaker proposition: every even number large enough can be expressed as the sum of two natural numbers with prime factors of m and n, which is abbreviated as "m+n" 50010.0000000000105. In the next 20 years, mathematicians have successively proved that "7+7" 1956 China mathematician Wang Yuan proved "3+4" and later.