It is said that after Pythagoras invented Pythagoras theorem, he made an exception and killed one hundred cows, and held a "Hundred Cows Festival" to invite people from all over the city to celebrate.
There is a popular poem like this: "Pythagoras discovered famous people and held a famous Hundred Bulls Festival for this." In this festival, Pythagoras gave a speech and described a picture to people: points are generated by numbers, lines are generated by points, plane graphics are generated by lines, and three-dimensional graphics are generated by plane graphics. All objects perceived by three-dimensional graphics generate four elements: water, fire, earth and air.
These four elements are transformed into each other in various ways, creating a living, spiritual and spherical world. To know the world is to know the numbers that dominate the world.
Once, Pythagoras passed by the blacksmith's shop, and the harmonious voice of the blacksmith attracted him while he was striking the iron. He stood listening for a long time and found that the sound was related to the weight of the hammer.
Therefore, he compared the proportional relationship between different harmonics emitted by hammers with different weights, thus determining the mathematical relationship of various tones and discovering the theory of cosmic harmony from music and sound. Gamov, a famous scholar, once said: "This discovery is probably the first mathematical formula, which can be regarded as the first step in the development of theoretical physics."
It is said that Pythagoras designed a coin in Croton, and he was the first person to introduce this currency into South Italy. The coin has a positive city emblem on the front, several main letters of the city name on the circumference, and the same pattern on the other side, but with a negative color.
These coins reflect Pythagoras' view that "the position relationship between the upper and lower parts of the universe and the central part is the same, but opposite to each other". Once, Pythagoras talked with Ryan, the ruler of Phobos. Ryan praised his genius and eloquence and asked what his skills were.
Pythagoras replied, "I am not a master of skills, but a man (philosopher) who loves wisdom." He first proposed that philosophers are not "wise men" but "people who love wisdom" and that philosophy is "the pursuit of wisdom".
Spectator Greek philosophy is a spectator. Pythagoras once had such a metaphor: there are three kinds of people in this world, just as there are three kinds of people who come to see the Olympic Games.
Those who come to do business belong to the lowest class, and those who are taller than them come to win the championship. However, the tallest one is the person who just came to see it.
Similarly, in life, some people work for fame and fortune, while others are slaves of money. However, a few people made the best choice. They spend their energy and time thinking about nature and engaging in scientific research. This is a philosopher. Pythagoras said when talking with people about whether women are worthy of respect: "They have three sacred names, first they are called virgins, then they are called brides, and finally they are called mothers."
The Soul of a Friend Once, when Pythagoras was wandering, he saw a man hitting a dog. He showed great pity and snapped, "stop, don't hit it, because I recognize its voice." The soul of a friend of mine is attached to it. " It is said that Pythagoras has the power to dominate wild animals.
A female bear has caused terror to the residents near Dornia. He went to education and finally made her obey, no longer harassing creatures, only eating fruit and honey cakes. Once, he persuaded a cow to stop eating broad beans as a reward. Pythagoras rescued it from the slaughterhouse and gave it to the temple of Hera in Tarant for feeding.
He can also calm storms, eliminate earthquakes and stop epidemics. One day, when he passed by casas, the river saluted him loudly.
This frightened all the people present. Abalis, a descendant of God, was an old priest in the temple of Apollo in the far north. He climbed mountains and mountains, begging for alms for temples along the way.
When Croton saw Pythagoras, he immediately recognized that this was God and gave the arrow to Pythagoras. Pythagoras accepted the gift, and in return, he showed Abalis his golden leg-a piece of tonglaijin leaf on Pythagoras' thigh, and said: I am a descendant of the sun god, and I have come down to save mankind. You should help me.
So Abalis donated all his property to the Pythagorean Union. Pythagoras, the "sage", spent some time in an underground cave on his way to Italy.
After a while, Pythagoras came out of the cave, and his figure became shriveled and looked like a skeleton. Then he went to * * * to claim that he had been to hades, and even told them his experience. Those people were moved to tears, and even cried and regarded him as a saint.
Those people even sent their wives to him, hoping to learn some of his teachings. Therefore, they are also called women of Pythagoras.
Several fishermen have just caught a big net of fish. When Pythagoras met them at the seaside, he immediately told them how many fish were in the net, and the figures were extremely accurate. Then he bought them with money and threw them all into the sea. The miracle spread before he arrived in Dacroton.
Soon, he became famous in the school there. Pythagoras and his school regard beans as sacred, and it is forbidden to eat them on foot.
One day around 500 BC, Pythagoras and his disciples were giving lectures at Miro's house. A noble disciple named Julong was resentful because Pythagoras refused to join the club and incited a group of people to set fire to the house. Pythagoras escaped from the fire with the help of his disciples. When they fled to a bean field and stopped, he would rather be arrested than trample on it in violation of trade union regulations.
In this way, he was killed by the pursuers. It is also said that he fled to Metaponda for refuge, fasted for 40 days and died in the Muse Temple.
2. A little math knowledge
Archimedes 1, sand calculation, is a book devoted to the study of calculation methods and theories.
Archimedes wanted to calculate the number of grains of sand in a big sphere full of the universe. He used a very strange imagination, established a new counting method of order of magnitude, determined a new unit, and put forward a model to represent any large number, which is closely related to logarithmic operation. 2. Using 96 circumscribed circles and inscribed circles to measure the circle, the pi is 3.1408 3. By skillfully using exhaustive method, it is proved that the surface area of the ball is equal to four times the area of the great circle of the ball; The volume of a ball is four times that of a cone. The base of this cone is equal to the great circle of the ball, which is higher than the radius of the ball.
Archimedes also pointed out that if there is an inscribed sphere in an equilateral cylinder, the total area of the cylinder and its volume are the surface area and volume of the sphere respectively. In this book, he also put forward the famous "Archimedes axiom".
4. "Parabolic quadrature method", which studies the quadrature problem of curves and figures, and establishes a conclusion by exhaustive method: "Any arch (i.e. parabola) surrounded by the section of a straight line and a right-angled cone is four-thirds of the area of a triangle with the same base height." He also verified this conclusion again by mechanical weight method, and successfully combined mathematics with mechanics.
5. On Spiral is Archimedes' outstanding contribution to mathematics. He made clear the definition of spiral and the calculation method of spiral area.
In the same book, Archimedes also derived the geometric method of summation of geometric series and arithmetic series. 6. Plane balance is the earliest treatise on mechanical science, which is about determining the center of gravity of plane graphics and three-dimensional graphics.
7. Floating Body is the first monograph on hydrostatics. Archimedes successfully applied mathematical reasoning to analyze the balance of floating body, and expressed the law of floating body balance with mathematical formula. 8. On the cone and sphere, it is about determining the volume of the cone formed by parabola and hyperbola rotation and the volume of the sphere formed by ellipse rotation around its long axis and short axis.
Pythagorean Theorem 1 Pythagorean Theorem: Anyone who has studied algebra and geometry will hear about Pythagorean Theorem. This famous theorem is widely used in many branches of mathematics, architecture and measurement. The ancient Egyptians used their knowledge of this theorem to construct right angles. They tie ropes every 3, 4 and 5 units. Then straighten the three ropes to form a triangle. They know that the diagonal of the largest side of a triangle is always a right angle (32+42=52). Pythagoras theorem: given a right triangle, the square of the hypotenuse of the right triangle is equal to the sum of the squares of the two right sides of the same right triangle. And vice versa: if the sum of squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle. Although this theorem was named after the Greek mathematician Pythagoras (about 540 BC), there is evidence that the history of this theorem can be traced back to the era of Hammurabi in ancient Babylon 1000 years ago. The name of this theorem is attributed to Pythagoras. Probably because he was the first to record the certificate he wrote at school. The conclusion of Pythagoras theorem and its proof spread all over the world in all continents, cultures and periods. In fact, this theorem has been proved more than any other discovery! 2. The Pythagorean school holds that any number can be expressed as an integer or a ratio of integers. But a student named Hibbs found that if the side length of an isosceles right triangle is 1, then according to the Pythagorean theorem (that is, Pythagorean theorem, which is just called in the west, it was actually discovered by our ancestors first! . ), the square of the hypotenuse length should be 1+ 1=2, and the number with the square equal to 2 cannot be expressed by integers or fractions.
He told others about this discovery, but this discovery overthrew the basic idea of the "Bi" school. So he was thrown into the river and executed.
Later, people affirmed this discovery and named it irrational number to distinguish Bipai's rational number. Memory of irrational numbers √ 2 √ 1.4 1: only meaningful √ 3 √ 1.7320: laying goose eggs together √ 5 √ 2.2360679: two geese laying six eggs (delivering babies) and six wives and uncles √ 7 √ 2.64579.
3. 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, and restated them in the form of propositions, which 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" 50010.000000000105. In the next 20 years, mathematicians successively proved that "7+7" 1956 China mathematician Wang Yuan proved "3+4" and later.
4. Math tips
Goldbach conjecture About 250 years ago, the German mathematician Goldbach discovered that any integer greater than 5 can be expressed as the sum of three prime numbers.
He verified many figures, and this conclusion is correct. But he couldn't find any method to prove it completely in theory, so he wrote a letter on June 7, 742/kloc-0, asking Euler, a famous mathematician who worked at the Berlin Academy of Sciences at that time.
Euler seriously thought about this problem. He first checked a long numerical table one by one: 6 = 2+2+2 = 3+38 = 2+3+3 = 3+59 = 3+3+3 = 2+710 = 2+3+5 = 5+51/kloc. 38+07+7 1=97+3 10 1=97+2+2 102=97+2+3=97+5 …… 。
Extended Goldbach conjecture About 250 years ago, German mathematician Goldbach discovered a phenomenon that any integer greater than 5 can be expressed as the sum of three prime numbers. He verified many figures, and this conclusion is correct.
But he couldn't find any method to prove it completely in theory, so he wrote a letter on June 7, 742/kloc-0, asking Euler, a famous mathematician who worked at the Berlin Academy of Sciences at that time. Euler seriously thought about this problem.
He first checked a long numerical table one by one: 6 = 2+2+2 = 3+38 = 2+3+3 = 3+59 = 3+3+3 = 2+710 = 2+3+5 = 5+51/kloc. 38+07+71= 97+310/= 97+2102 = 97+2+3 = 97+5 ... This table can be expanded infinitely, and every expansion increases Euler's confidence in affirming Goldbach's conjecture. And he found that the problem of proof should actually be divided into two parts.
That is, it is proved that all even numbers greater than 2 can always be written as the sum of two prime numbers, and all odd numbers greater than 7 can always be written as the sum of three prime numbers. When he finally believed that this conclusion was true, he wrote back to Goldbach on June 30th.
The letter said: "Any even number greater than 2 is the sum of two prime numbers. Although I can't prove it yet, I am sure it is completely correct. " Because Euler is a famous mathematician and scientist, his self-confidence has attracted and inspired countless scientists to try to prove it, but there was still no progress until the end of 19. This seemingly simple but extremely difficult problem of number theory has long plagued the mathematics community.
Whoever can prove it can climb a lofty and strange mountain in the kingdom of mathematics. So some people compare it to "a pearl in the crown of mathematics".
In fact, a large number of numbers have been verified, and the verification of even numbers has reached more than 6543.8+0.3 billion, and no counterexample has been found. So why can't this question be concluded? This is because there are infinitely many natural numbers, and no matter how many numbers are verified, it cannot be said that the next number must be like this.
The rigor and precision of mathematics should give scientific proof to any theorem. So Goldbach's conjecture has not become a theorem for hundreds of years, which is why it is famous as a conjecture.
There are several different ways to prove this problem. One of them is to prove that a number is the sum of two numbers, in which the prime factor of the first number does not exceed A and the prime factor of the second number does not exceed B. This proposition is called (a+b).
The ultimate goal is to prove that (a+b) is (1+ 1). 1920, Professor Brown, a Norwegian mathematician, proved by ancient screening method that any even number greater than 2 can be expressed as the sum of the products of nine prime numbers and nine other prime numbers, that is, it proved that (a+b) is (9+9).
1924, German mathematicians proved (7+7); 1932, the British mathematician proved (6+6); 1937, the Soviet mathematician vinogradov proved that an odd number large enough can be expressed as the sum of three odd prime numbers, from which the conclusion of the odd part of Euler's vision was drawn, leaving only the proposition of the even part. 1938, China mathematician Hua proved that almost all even numbers can be expressed as the sum of the powers of a prime number and another prime number.
From 1938 to 1956, Soviet mathematicians successively proved (5+5), (4+4) and (3+3). 1957, China mathematician Wang Yuan proved (2+3); 1962, China mathematician Pan Chengdong and Soviet mathematician Barba independently proved (1+5); 1963, Pan Chengdong, Wang Yuan and Barba proved this point again (1+4).
1965, several mathematicians proved at the same time (1+3). 1966, Chen Jingrun, a young mathematician in China, made an important improvement on the screening method and finally proved it (1+2).
His proof shocked China and foreign countries, and he was praised as "pushing the mountain" and named it "Chen Theorem". He proved the following conclusion: any large enough even number can be expressed as the sum of two numbers, one of which is a prime number, and the other is either a prime number or a product of two prime numbers.
Put it away.
5. Why is Pythagoras important?
It is believed that Pythagoras coined the word "philosophy".
Pythagoras was born in Samos, but settled in Croton. He founded an association in Croton, which is also a school, a way of life and a set of philosophical and political beliefs.
Pythagoras found that the intervals marked by the four fixed strings on the lyre can be expressed by the ratio of the number 1, 2, 3 and 4. This important discovery forms the basis of the concept of music harmony.
Pythagoras further explained how numbers reflect natural phenomena such as celestial movements. Pythagoras had a profound influence on mathematics, because mathematics is the language of modern physics.
Pythagoras and his followers are also interested in numerology and theories about the mysterious meaning of numbers. They believe that music is the soul of numbers, and proper behavior-such as daily habits, eating, playing musical instruments, etc. -can make people listen to music from the sky.
They are all strict vegetarians and fast broad beans.
6. What contribution did Pythagoras make to mathematics?
Pythagoras was a famous philosopher, mathematician and astronomer in ancient Greece and the founder of Pythagoras order.
In about 532 BC, in order to escape Samos' brutal rule, he moved to southern Italy and established an ethics and political college in Klotong (now Clauteaux). Pythagoras' contribution lies in his theory that mathematics plays an important role in the objective world and music, and expounds the relationship between the musical tone and the length of Danxian.
Other mathematical principles and discoveries attributed to him include: the incommensurability of the sides and diagonals of a square, the pythagorean theorem of a right triangle, etc. They may have been put forward by Pythagoras school when mathematical concepts developed to a higher stage.
7. Who knows the famous mathematical sayings?
1. Percentage of Wang Juzhen
Wang Juzheng, a scientist in China, has a motto about the failure of the experiment, which is called "There is still a 50% hope of success if you continue, and 1000% failure if you don't do it."
2. Tolstoy's music score
Tolstoy, a great Russian writer, compared people to a score when talking about people's evaluation. He said: "A person is like a score, his practical ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the score. "
1, the essence of mathematics is its freedom. A poet and lead singer
2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. A poet and lead singer
3. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity, but no other concepts need to be clarified as infinity. Hilbert (Hilbert)
Mathematics is an infinite science. Herman Weil
5. Problem is the core of mathematics. Halmos
6. As long as a branch of science can raise a large number of questions, it is full of vitality, and no questions indicate the termination or decline of independent development. Hilbert
7. Some beautiful theorems in mathematics have the following characteristics: they are easy to be summarized from facts, but their proofs are extremely hidden. Gauss
3. Rybakov constant and variables
Russian historian Rybakov said in The Use of Time: "Time is a constant, but for diligent people, it is a' variable'. People who use' minutes' to calculate time spend 59 times more time than people who use' hours'. "