A Brief Introduction to the Life and Major Scientific Achievements of Euclid and Archimedes

Date of birth and death: 287-2 BC12.

Introduction:

The great mathematician and mechanic of ancient Greece.

Born in Syracuse, Sicily, died in the same place.

Alexander studied with Euclid's students in the cultural center at that time, and later kept close contact with Alexander's scholars, so he was a member of the Alexandria School. Later generations spoke highly of Archimedes, and often ranked him with I Newton and C·F· Gauss as the three greatest mathematicians in history. His life is not recorded in detail, but many stories about him are widely circulated.

Life:

Archimedes (287-2 12 BC) was born in a small village near Syracuse, Greece. He was born into a noble family, and was related to King Hilong of Syracuse, and his family was very rich. Archimedes's father was an astronomer and mathematician, knowledgeable and humble. Influenced by his family, Archimedes became interested in mathematics, astronomy, especially ancient Greek geometry. When he was just eleven years old, with the help of his relationship with the royal family, he was sent to study in Alexandria, Egypt. Alexandria, located at the mouth of the Nile, was one of the centers of cultural trade at that time. There are magnificent museums, libraries and talented people here, which are praised as "the capital of wisdom" by the world. Archimedes studied and lived here for many years and had close contacts with many scholars. He absorbed the excellent cultural heritage of the East and ancient Greece and made great contributions to his later scientific career. In 2 12 BC, Roman troops invaded Syracuse, and Archimedes was killed by Roman soldiers at the age of 75. Archimedes' body is buried in Sicily, and the tombstone is engraved with a figure of a cylinder engraved with a ball to commemorate his outstanding contribution to geometry. Archimedes' achievements

Archimedes is undoubtedly the greatest mathematician and scientist produced by ancient Greek civilization. His outstanding contributions in many scientific fields earned him the high respect of his contemporaries.

Archimedes worked out the areas and volumes of parabolic bows, spirals and circles, as well as the volumes of complex geometric bodies such as ellipsoids and paraboloids. In the process of deriving these formulas, he skillfully used the "exhaustive method", which is what we call the method of gradually approaching the limit today, so he is recognized as the originator of calculus calculation. In this way, he also estimated that the value of ∏ was between and got the solution of cubic equation. Facing the tedious numerical representation in ancient Greece, Archimedes put forward an important method for calculating grades and used it to solve many mathematical problems. Archimedes made the most outstanding achievements in mechanics, mainly focusing on statics and hydrostatics. In the process of studying machinery, he discovered the lever principle and used this principle to design and manufacture many machines. He discovered the law of buoyancy in the process of studying floating bodies, which is also known as Archimedes principle.

Archimedes also made outstanding achievements in astronomy. He designed some balls and connected them with strings and sticks to imitate the movements of the sun, the moon and the stars, and made them rotate by water power. In this way, solar and lunar eclipses can be vividly displayed. Archimedes thought that the earth was spherical and revolved around the sun, which was earlier than Copernicus' Heliocentrism 1800 years. Limited by the conditions at that time, he did not make a thorough and systematic study on this issue. But it is remarkable to put forward such an opinion as early as the third century BC. Archimedes has many works. As a mathematician, he wrote many mathematical works, such as about spheres and cylinders, about cones and spheres, about parabola quadrature, about spirals and so on. As a mechanic, he wrote many mechanical works, such as On the Balance of Flat Plate, On Floating Body, On Lever, On Center of Gravity and so on. In the book On the Balance of Flat Plates, he systematically demonstrated the lever principle. When discussing floating bodies, he demonstrated the law of floating bodies.

Archimedes is not only brilliant in theory, but also an engineer with practical spirit. He designed and manufactured many institutions and machines in his life. In addition to the lever system, it is worth mentioning that there are weight lifting pulleys, irrigation machines, water pumps and military projectors. The water pump, known as Archimedes' water lifting screw, was invented to drain water from the cabin of a big ship. The water pump can be carried to a high place through the screw handle, which has been widely used in Egypt and is the predecessor of modern screw pump. "Give me a fulcrum, and I can move the earth."

Archimedes is not only a theorist, but also a practitioner. Throughout his life, he was keen on applying his scientific discoveries to practice, thus combining the two. In Egypt around 1500 BC, people used levers to lift heavy objects, but people didn't know why. Archimedes devoted himself to this phenomenon and discovered the lever principle.

King Hennon always doubted Archimedes' theory. He asked Archimedes to turn them into living examples to convince people. Archimedes said, "Give me a fulcrum and I can move the earth." The king said, "I'm afraid this can't be realized." You'd better help me tow that big boat on the coast. " This ship was built by King Henon for the king of Egypt. It is big and heavy, and has been stranded on the coast for many days because it can't move. Archimedes readily promised. Archimedes designed a complicated lever pulley system to be installed on the ship, and handed one end of the rope to King Henon. King Hennon gently pulled the rope, and a miracle appeared. The ship moved slowly and finally sank into the sea. The king was surprised and admired Archimedes very much. He sent someone to post a notice saying, "In the future, no matter what Archimedes says, you must believe him."

Mystery of golden crown

King Hennon asked the goldsmith to make a pure gold crown for him. After it was done, the king suspected that the craftsman had mixed silver into the crown, but the crown was as heavy as the pure gold given to the goldsmith at the beginning. Did the craftsman play tricks? The problem of trying to test the authenticity without destroying the crown not only stumped the king, but also made the ministers look at each other. Later, the king gave it to Archimedes. Archimedes thought hard about many methods, but all failed. One day, he went to the bathhouse to take a bath. Sitting in the bathtub, he saw the water overflowing and felt his body being gently pulled up. He suddenly realized that he jumped out of the bathtub and went straight to the palace without clothes on. He shouted "Eureka" and "Eureka" all the way. It turns out that if the crown is put into water, the amount of water released is not equal to the amount of water released by the same weight of gold, and it must be mixed with other metals. This is the famous law of buoyancy, that is, an object immersed in a liquid is subjected to upward buoyancy, and its size is equal to the weight of the liquid discharged by the object. Later, this law was named Archimedes principle.

Patriot Archimedes

In his later years, the Roman army invaded Syracuse, and Archimedes instructed his compatriots to make many weapons for attack and defense. When Marcelle Sai, the leader of the invading army, led a group of people to attack the city, he designed a trebuchet to beat the enemy out of the water. His crane with iron claws can lift the enemy ship, turn it upside down and throw it into the depths of the sea. Legend has it that he also led the people of Syracuse to make a huge concave mirror, which focused the sunlight on the approaching enemy ship and made it burn. Roman soldiers have been frightened by such frequent blows. They are afraid of everything. As soon as they saw the rope or wood thrown from the city, they exclaimed "Archimedes is coming" and then ran around. Roman troops were kept out of the city for three years. Finally, in 2 12 BC, the Romans took advantage of the slight relaxation of the ancient city of Syracuse to attack on a large scale and break into the city. At this time, Archimedes was studying a profound math problem. A Roman soldier broke into the house and trampled on his drawing with his foot. Archimedes argued with him angrily. The cruel soldier refused to listen, only to see a brilliant scientific superstar fall with a wave of his hand.

Rumors and contributions about him:

It is said that after he established the lever law of mechanics, he once issued a magnificent statement: "Give me a foothold and I can move the earth!" " King Shiloh of Syracuse asked the goldsmith to make a crown out of pure gold. Because it was suspected that there was silver in it, Archimedes was asked to identify it. 朐∨朐? The water overflowed from the basin, so I realized that although objects made of different materials have the same weight, the discharged water will not be equal because of their different volumes. According to this truth, it can be judged whether the crown is adulterated. Archimedes jumped up with joy and ran home naked, shouting, "Found it! Found it. " (Greek means "I found it") In his famous book On Floating Bodies, he summed up the basic principle of hydrostatics, that is, the weight of an object in a liquid is equal to the weight of the liquid, and later became famous for Archimedes' principle. During the Second Punic War, the Roman army besieged Syracuse, and Archimedes devoted all his intelligence to serving the motherland. Legend has it that he grabbed the enemy's boat with a crane and smashed it to pieces; Invent wonderful machines and fire big stones and fireballs. There are also some books that record that he burned enemy ships with huge fire mirrors reflecting sunlight, which is probably an exaggeration. In a word, he tried his best to give the enemy a heavy blow. Finally, Syracuse Gui was betrayed by spies and ran out of food. Archimedes died unfortunately at the hands of Roman soldiers. Archimedes' handed down works mainly include the following works. On the Ball and the Cylinder is his masterpiece, which contains many great achievements. Starting from several definitions and axioms, he deduced more than 50 propositions about the area and volume of spheres and cylinders. The balance of plane figure or its center of gravity, based on several basic assumptions, demonstrates the mechanical principle with strict geometric methods, and finds out the centers of gravity of several plane figures. The sand counter designs a method that can represent any large number, which corrects the wrong view that sand is uncountable, and even if it can be counted, it can't be represented by arithmetic symbols. On the floating body, the buoyancy of the object is discussed and the stability of the rotating projectile in the fluid is studied. Archimedes also put forward a "herd problem", which contains eight unknowns. Finally, it comes down to a quadratic indefinite equation. The number of its solutions is amazing, * * * more than 200,000 digits!

It is doubtful whether Archimedes solved this problem at that time. In addition, there is a very important work, which is a letter to Eratosthenes, the content of which is to explore ways to solve mechanical problems. This is a scroll of parchment manuscript discovered by Danish linguist J.L. Heiberg in 1906. Originally written in Greek, it was later erased and rewritten in religious words. Fortunately, the original handwriting was not wiped clean. After careful identification, it was confirmed to be Archimedes' work. Some of them have seen it in other places, and some people think it has disappeared in the past. Later, it was published internationally in the name of Archimedes Law. This paper mainly talks about the method of finding problems according to mechanical principles. He regards an area or volume as something with weight, divides it into many very small strips or pieces, then balances these "elements" with the known area or volume, finds the center of gravity and fulcrum, and can use the lever law to calculate the required area or volume. He regards this method as a tentative work before strict proof, and will prove it by reducing to absurdity after getting the result. In this way, he achieved many brilliant achievements. Archimedes' method has the idea of modern integral theory. However, he did not explain whether this "element" is finite or infinite, nor did he get rid of the dependence on geometry, let alone use the limit method. Nevertheless, his thought is of epoch-making significance and is the pioneer of modern integral calculus. He has many other inventions. No ancient scientist, like Archimedes, combined skillful calculation skills with strict proof, and closely combined abstract theory with concrete application of engineering technology.

Later, Archimedes became a great scholar who was both a mathematician and a mechanic, enjoying the reputation of "the father of mechanics". The reason is that he discovered the lever principle through a lot of experiments, and then deduced many lever propositions through geometric derivation and gave strict proofs. Among them is the famous Archimedes principle, and he has also made brilliant achievements in mathematics. Although there are only a dozen works by Archimedes, most of them are geometric works, which have played a decisive role in promoting the development of mathematics. 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. In the measurement of a circle, using the circumscribed circle and the inscribed 96-sided circle, the pi is 22/7.