Mathematical celebrities

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, with the help of his relationship with the royal family, he was sent to Alexandria, the cultural center of ancient Greece. He studied under Euclid's students erato Sese and Cannon, and he kept close contact with scholars in Alexandria in the future, so he was a member of the Alexandria School.

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, he 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.

[Edit this paragraph] Scientific achievements

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

Mechanically:

Archimedes made the most outstanding achievements in mechanics.

1. Archimedes systematically studied the center of gravity and lever principle of objects on the basis of summarizing the experience of Egyptians lifting heavy objects with levers. This paper puts forward a method to accurately determine the center of gravity of an object, and points out that if it is supported in the center of the object, it can keep the object in balance. At the same time, in the process of studying machinery, he discovered and systematically proved Archimedes principle (that is, lever law), which laid the foundation of statics. In addition, Archimedes 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' mathematical achievement lies in that he not only inherited and carried forward the scientific method of studying abstract mathematics in ancient Greece, but also linked the research of mathematics with practical application. Archimedes

1, Archimedes' calculation method for determining the area of parabola bow, helix and circle, and the surface area and volume of complex geometric bodies such as ellipsoid and paraboloid. In the process of deriving these formulas, he founded the "exhaustive method", which is similar to the method of gradually finding the limit in modern calculus.

He is the first person to study pi scientifically. He proposed to calculate pi by increasing the number of sides and approaching the areas of inscribed polygons and circumscribed polygons. He calculated the range of pi: 223/7 1

3. Facing the tedious numerical representation in ancient Greece, Archimedes also pioneered the method of memorizing large numbers, which broke through the restriction that the number of Greek letters at that time could not exceed 10,000, and used it to solve many mathematical problems.

4. The famous Archimedes axiom is put forward and expressed in modern mathematical language. Archimedes principle means that for any natural number (excluding 0)a and B, if A; b.

Astronomy:

1, he invented the planetarium driven by water conservancy, and used it to simulate the movements of the sun, planets and the moon and perform an eclipse of the sun and the moon;

2. He 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.

Archimedes spiral perpetual motion machine

Pay attention 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 the weight lifting pulley, water pump and military trebuchet. The water pump known as Archimedes Screw is still used in Egypt and other places.

[Edit this paragraph] Works

There are more than 10 mathematical works handed down by Archimedes, most of which are Greek manuscripts. His works focus on the quadrature problem, mainly the area of curve graphics and the volume of curve cube. Its style is deeply influenced by Euclid's Elements of Geometry. First, some definitions and assumptions are established, and then they are proved in turn.

As a mathematician, he wrote some mathematical works, such as On Sphere and Cylinder, Measurement of Circle, Quadrature of Parabola, On Spiral, On Cone and Sphere, Calculation of Sand, etc. 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 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.

List of works:

Sand meter is a book devoted to 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.

"Measurement of a circle", using 96 circumscribed circles and inscribed circles, it is found that the pi is 223/7 1

On balls and cylinders, it is proved that the surface area of the ball is equal to four times the area of the great circle of the ball by skillfully using the exhaustive method. 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".

"Parabolic quadrature method" studies the quadrature problem of curves and figures, and draws a conclusion by exhaustive method: "The area of any arch (i.e. parabola) surrounded by the sections of straight lines and right-angled cones 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.

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.

The balance of parallel graphics or its center of gravity is the earliest mechanical science work, which is about determining the center of gravity of plane graphics and three-dimensional graphics.

On Floating Bodies 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. In the book, he studied the stability of rotating projectiles in fluid.

"On Cones and Spheres" is about determining the volume of cones formed by parabolas and hyperbolas, and the volume of spheres formed by ellipses rotating around their major and minor axes.

Archimedes method is a letter to Eratosthenes, which is mainly based on mechanical principles to find solutions to problems. He regards this method as a tentative work before strict proof, and will prove it by reducing to absurdity after getting the result.

The cattle problem contains eight unknowns, which ultimately comes down to a quadratic indefinite equation. It was first put forward in a letter to Eratosthenes, but its authenticity is quite doubtful. The "sheep problem" probably existed a long time ago, and Archimedes just studied it again.

[Edit this paragraph] Story

Note: The authenticity of Archimedes' story has not been verified yet.

Discovery of buoyancy principle

There is a legend about the principle of buoyancy.

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. Until modern times, people are still using this principle to calculate the specific gravity of objects and determine the load capacity of ships.

The story about the principle of leverage-"Give me a fulcrum and I can move the earth"

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.

No one could explain the lever principle before Archimedes discovered it. At that time, when talking about this issue, some philosophers insisted that it was "magic". However, Archimedes denied what "magic" was.

After Archimedes established the lever law, he concluded that any heavy object can be lifted with little force as long as the appropriate lever length can be obtained. It is said that he once said such grandiloquence: "Give me a fulcrum and I can lift the earth." King Syracuse listened and said to Archimedes, "In the name of Zeus, what you said is really strange, Archimedes!" " After Archimedes explained the characteristics of lever to the king, the king said, "Where can I find a fulcrum to pry up the earth?"

"There is no such fulcrum." Archimedes replied.

"So, it is impossible to convince people of the divine power of mechanics?" Said the king.

"No, no, you misunderstood, your majesty. I can give you other examples. " Archimedes said.

The king said, "You are too boastful! Why don't you help me push something that heavy and see what you say? " At that time, the king had a problem, which was to build a very big ship for the king of Egypt. After the ship was built, the whole city of Syracuse was mobilized, and it was impossible to push it into the water. Archimedes said, "Well, I'll push the boat for you."

After Archimedes left the king, he used the principle of lever and pulley to design and manufacture a set of exquisite machinery. When everything was ready, Archimedes invited the king to watch the ship launch. He gave the end of a thick rope to the king to pull gently. Suddenly, the big ship moved slowly and slipped into the water smoothly. When the king and ministers saw such a miracle, they were as surprised as if they were watching magic! So the king persuaded Archimedes and issued a notice to the whole country: "From now on, no matter what Archimedes says, you must believe him ..."

Defend Syracuse

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 ... Archimedes.

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.

[Edit this paragraph] Grave

Roman general marcellus was deeply saddened by Archimedes' death. In addition to dealing with the soldier seriously, he also found Archimedes' relatives, gave him pensions and tributes, and built a tomb for Archimedes to show his respect. As a memorial, Archimedes found that the volume and surface area of a sphere are two-thirds of that of a circumscribed cylinder. Before his death, he expressed his wish to carve this figure on the tomb.

Later, things changed, and the ancient Syracuse didn't know how to cherish this extraordinary monument. More than 65,438+000 years later (75 BC), Cicero (65,438+006-43 BC), a famous Roman politician and writer, served as a financial official in Sicily and wanted to pay tribute to this great man's tomb, but the local residents denied its existence. People use it. I found a small cylinder with several balls and cylinder patterns engraved on it. This long-forgotten lonely grave was finally found. The epitaph is still faintly visible, and about half of it has been corroded by wind and rain. More than two thousand years have passed, and with the passage of time, this tomb has disappeared without a trace. Now there is an artificially carved grotto, about 10 meters wide and covered with moss, which is said to be the tomb of Archimedes.

[Edit this paragraph] Impact and assessment

Archimedes is a great mathematician and mechanic and enjoys the reputation of "the father of hydrostatics". He discovered the lever principle through a lot of experiments, and deduced many lever propositions by geometric methods, and gave strict proofs, including the famous Archimedes principle (lever principle).

Archimedes

He has also 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 the essence of his thought extends to the increasingly mature infinitesimal analysis field in17th century, and indicates the birth of calculus.

Because of his outstanding contribution, American E.T. Bell used mathematical figures to evaluate Archimedes: Any open list of the three greatest mathematicians of all time will definitely include Archimedes, while the other two are usually isaac newton and C.F. Gauss. However, compared with its brilliant achievements and background of the times, or its far-reaching influence on the present and future generations, Archimedes should be the first to be promoted.

Except isaac newton and Albert Einstein, no one has made such a great contribution to human progress 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 Galilei in the Renaissance took him as a model.