Archimedes (about 287 ~ 2 BC12) was a physicist and mathematician in ancient Greece and the founder of statics and hydrostatics.

Archimedes' life

In 287 BC, Archimedes was born in Syracuse, Sicily (now Syracuse, Italy). He was born into a noble family and was related to Hennon, king of Syracuse. His family is very rich. Archimedes's father was an astronomer and mathematician, knowledgeable and humble. At the age of eleven, he was sent to study in Alexandria, the cultural center of ancient Greece, with the help of his relationship with the royal family.

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 was interested in mathematics, mechanics and astronomy during his study. When he was studying astronomy, he invented a planetary instrument driven by water conservancy, and used it to simulate the movement of the sun, planets and the moon and perform an eclipse of the sun and the moon. In order to solve the problem of irrigating land with Nile water, it invented a cylindrical spiral water lifter, which was later called "Archimedes spiral".

In 240 BC, Archimedes returned to Syracuse and became a consultant to King Henon, helping him solve various scientific and technological problems in production practice, military technology and daily life.

In 2 12 BC, the Roman army captured Syracuse, and Archimedes, who was absorbed in scientific problems, was unfortunately killed by outrageous 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' scientific achievements

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

Mechanics: Archimedes made the most outstanding achievements in mechanics. He systematically and strictly proved the lever law and laid the foundation of statics. Archimedes systematically studied the center of gravity and lever principle of an object on the basis of summarizing the experience of predecessors, put forward a method to accurately determine the center of gravity of an object, and pointed out that supporting it in the center of the object can keep the object in balance. In the process of studying machinery, he discovered the law of lever 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.

Geometry: Archimedes' calculation method for determining the area of parabola bow, helix and circle, and the surface area and volume of ellipsoid, paraboloid and other complex geometric bodies. In the process of deriving these formulas, he founded the "exhaustive method", which is what we call the method of gradually approaching the limit today, and is therefore recognized as the originator of calculus calculation. He calculated pi more accurately by increasing the number of sides and approximating the areas of inscribed polygons and circumscribed polygons. Facing the tedious numerical representation in ancient Greece, Archimedes also pioneered the method of memorizing large numbers, which broke through the restriction that Greek letters could not exceed 10 thousand at that time and solved many mathematical problems with it.

Astronomy: Archimedes also made outstanding achievements in astronomy. In addition to the planetary instruments mentioned above, he also thinks that the earth is spherical and revolves around the sun, which is 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.

Writings: There are more than 10 mathematical works handed down by Archimedes, most of which are Greek manuscripts. His works focus on quadrature problems, mainly the area of curved edges and the volume of curved cubes. His style is deeply influenced by Euclid's Elements of Geometry. First, he established some definitions and assumptions, and then proved them in turn. As a mathematician, he wrote works about spheres and cylinders, the measurement of circles, the quadrature of parabolas, spirals, cones and spheres, and sand. As a mechanic, he wrote many mechanical works, such as On the Balance of Numbers, On Floating Bodies and On Lever and Principle.

Among them, On the Ball and Column is his masterpiece, including 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, starting from 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, exceeding 200,000 digits!

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.

Attach importance to practice: Archimedes is obviously different from the scientists in Athens, that is, he not only attaches importance to the rigor and accuracy of science, but also requires accurate logical proof of every problem; But also attaches great importance to the practical application of scientific knowledge. He attached great importance to experiments and made various instruments and machinery by himself. During his life, he designed and manufactured many institutions and machines. In addition to the lever system, it is worth mentioning that there are weight lifting pulleys, irrigation machines, water pumps and military trebuchets. The water pump known as Archimedes Screw is still used in Egypt and other places.

The story of Archimedes

"Give me a fulcrum and I will push 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. " At that time, King Hennon built a boat for the king of Egypt. It is big and heavy, and it 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."

The story of bathing

There is an interesting story about Archimedes. According to legend, King Guhennon of Silas asked craftsmen to make him a pure gold crown. When it was finished, the king suspected that the craftsman had mixed a fake gold crown, but the gold crown was as heavy as the pure gold originally given to the goldsmith. 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 asked Archimedes to test it. At first Archimedes was also thinking hard, to the point. One day, he went to the bathhouse to take a bath. Sitting in the bathhouse, he saw the water overflowing and felt his body being gently pulled up. He suddenly realized that the proportion of gold crowns can be determined by measuring the displacement of solids in water. He jumped out of the bathtub excitedly and ran out without even considering his clothes, shouting "found it!" Eureka! " . Eureka, which means "I see".

After further experiments, he came to the palace. He put the crown and pure gold with the same weight in two jars filled with water, and compared the water overflowing from the two jars, and found that the jar with the crown overflowed more water than the other jar. This shows that the volume of the crown is larger than that of pure gold with the same weight, so it proves that other metals are mixed in the crown.

The significance of this experiment is far greater than finding out that the goldsmith cheated the king. Archimedes discovered the law of buoyancy: the buoyancy gained by an object in a liquid is equal to the weight of the liquid it discharges. Later, this law was named Archimedes principle. Until modern times, people are still using this principle to calculate the specific gravity of objects and determine the load capacity of ships.

Patriot Archimedes

In his later years, the Roman army invaded Syracuse, and Archimedes instructed his compatriots to make many combat 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. The iron claw crane he made can lift and reverse enemy ships. ...

Another incredible legend is that he led the Syracuse people to hold the concave mirror, focused the sunlight on the wooden warships of the Roman army, and set them on fire. 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 defense of the ancient city of Sila to attack on a large scale. At this time, 75-year-old Archimedes was studying an abstruse math problem. A Roman soldier broke in and trampled on his painting with his foot. Archimedes argued with him angrily. The cruel and ignorant soldier raised his knife and a talented science superstar fell.

Archimedes' influence on later generations and his evaluation by later generations

Archimedes studied with Euclid's students in Alexandria, the cultural center at that time, and kept close contact with Alexandria's scholars, so he was a member of the Alexandria School.

Archimedes is a great mathematician and mechanic and enjoys 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 made brilliant achievements in mathematics, especially in geometry. His mathematical thought contains the idea of calculus. What he lacks is the concept of limit, but its essence extends to the field of infinitesimal analysis, and it is maturing in the17th century, which predicts the birth of calculus. Because of his outstanding contribution, American E.T. Bell commented on Archimedes in Mathematical Figures: Any open list of the three greatest mathematicians of all time will definitely include Archimedes, while the other two are usually Newton and Gauss. However, compared with his brilliant achievements and background of the times, or his far-reaching influence on contemporary and future generations, Archimedes should be the first to be respected.

Except the great Newton and the great Einstein, no one has made such a great contribution to the progress of mankind as Archimedes. Even Newton and Einstein used to draw wisdom and inspiration from him. He is "the ideal embodiment of the combination of theoretical genius and experimental genius", and Leonardo da Vinci and Galileo in the Renaissance followed his example.

Later generations often rank him with Newton and Gauss as the three greatest mathematicians in history. Archimedes was born in Syracuse, Sicily, at the southern tip of the Italian peninsula in 287 BC. Father is a mathematician and astronomer. Archimedes had a good family upbringing since childhood. 1 1 years old, was sent to study in Alexandria, the cultural center of Greece. In this famous city known as the "Capital of Wisdom", Archimedes Job collected books and learned a lot of knowledge, and became a protege of Euclid students erato Sese and Cannon, studying geometric elements.

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 play 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.