Go home. Born in Syracuse, Sicily. Archimedes has been to Alexandria. It is said that he invented Archimedes screw pump when he lived in Alexandria, and it is still used in Egypt today. During the Second Punic War, Roman troops besieged Syracuse, and finally Archimedes died at the hands of Roman soldiers. Archimedes was born in Silas, an ancient city at the southeastern tip of Sicily, Greece. At that time, the splendid culture of ancient Greece had gradually declined, and the economic and cultural center gradually moved to Alexandria, Egypt; On the other hand, the emerging Roman Empire on the Italian Peninsula is also expanding its power. There is also a new country, Carthage, rising in North Africa. Archimedes grew up in this era of alternating old and new forces, and the ancient city of Silas became a wrestling field for many forces. Archimedes's father was an astronomer and mathematician, so he was influenced by his family and loved mathematics very much. When he was about nine years old, his father sent him to study in Alexandria, Egypt. Alexandria was the center of knowledge and culture in the world at that time, and scholars gathered. The research on literature, mathematics, astronomy and medicine is very developed. Archimedes studied under many famous mathematicians here, including the famous geometry master Euclid, which laid the foundation for his future scientific research. [ 1]
Edit this paragraph of scientific research teaching
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? I want to test whether it is true or not. Archimedes discovered buoyancy.
You can't destroy the crown. This question 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 thought hard, too, to the point. One day, he was taking a bath at home. When he was sitting in the bathtub, he saw the water overflowing and felt his body being gently lifted. 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.
Lift a fulcrum of the earth.
Archimedes' study of machinery originated from his study in Alexandria. One day, after a long drought, Archimedes was walking along the Nile. He saw that it was quite difficult for farmers to carry water to irrigate their land. After thinking, he invented a principle of rotating water in a water pipe by spiral action.
The tool sucked up was called "Archimedes spiral water lifter" by later generations, and it was still used in Egypt after 2000. This tool became the ancestor of the propeller. In Europe at that time, some simple machines, such as screws, pulleys, levers and gears, were often used in engineering and daily life. Archimedes spent a lot of time studying and discovered the concepts of "lever principle" and "moment". For Archimedes, who often used tools to make machinery, it was easy to apply the theory to real life. He himself once said, "Give me a fulcrum and I can move the whole earth." It happened that King Havilon met another thorny problem: the king built a ship for King Ptolemy of Egypt. Because it is too big and heavy, it can't be put into the sea. The king said to Archimedes, "You can even lift the earth. Should it be okay to put the boat in the sea? " So Archimedes skillfully combined all kinds of machinery at once and built the machine. When everything was ready, he handed the rope of the tractor to the king. The king gave a gentle pull and the boat really went into the water. The king had to be impressed by Archimedes' genius. From this historical story, we can clearly know that Archimedes was probably the person who had the most thorough understanding of mechanical principles and applications in the world at that time.
Contemporary master of mathematics
For Archimedes, mechanical and physical research and inventions are only secondary, and he and Archimedes are more interested.
More time is spent on pure theoretical research, especially mathematics and astronomy. Mathematically, he calculated sphere area, sphere volume, parabola and ellipse area by "approximation method", and later mathematicians developed it into modern calculus based on this "approximation method". He even studied the properties of spiral curve, and today's "Archimedes spiral" curve is named in memory of him. In addition, he created a set of methods to remember large numbers in his book "Ganges Sand Count", which simplified the counting method. Archimedes elaborated on the principle of lever in his book On Lever (unfortunately lost). King Syracuse once doubted the power of leverage. He asked Archimedes to move a new three-masted ship full of heavy objects and passengers. Archimedes asked craftsmen to install a set of exquisitely designed pulleys and levers on the front, back, left and right sides of the ship. Archimedes told 100 people to grab a rope in front of the big ship. He asked the king to pull a rope, and the ship actually slipped slowly into the sea. The crowd cheered, and the king announced happily in public: "From now on, I ask everyone to believe Asmid no matter what they say!" " "Archimedes also used the sunlight gathered by parabolic mirrors to illuminate the Roman ships that invaded Syracuse and let them set themselves on fire. Many ships in Rome were burned, but the Romans could not find the cause of the fire. More than 900 years later, a scientist made a concave mirror according to Archimedes' method introduced in history books. He successfully set wood 45 meters away from the mirror and melted aluminum 42 meters away from the mirror. Therefore, many historians of science and technology usually regard Archimedes as the ancestor of human utilization of solar energy.
Astronomical research
He made a planetarium by hydraulic power, with the sun, moon, stars and five planets on the sphere. According to records, this planetarium not only runs accurately, but also can predict when the solar eclipse will happen. In his later years, Archimedes began to doubt the geocentric theory and speculated that the earth might revolve around the sun. This concept was not discussed until the Copernican era. At the end of the 3rd century AD, the Roman Empire and the Carthaginian Empire in North Africa fought for the hegemony of Sicily. Syracuse in Sicily has always taken refuge in Rome, but Carthage defeated the Roman army in 2 16 BC, and the new king of Syracuse (succeeded by the grandson of Xavier II) immediately turned the tables and made an alliance with Carthage, so the Roman Empire sent General Maceiras to attack Syracuse by sea and land at the same time. Archimedes saw the national crisis, and the sense of responsibility to defend his country prompted him to stand up against the enemy, so he racked his brains day and night. According to some later records, at that time, he built a huge crane, which could hang the enemy warships in mid-air, and then fell heavily on the water; At the same time, Archimedes also called on the people in the city to form a fan with mirrors, concentrate the sunlight on Roman warships and burn their ships (but the TV program "mythbusters" once experimented on this legend, and it turned out to be almost impossible to succeed); He also used the lever principle to make many trebuchets, and no enemy near the city wall could escape his flying stones or javelins. These weapons made the Roman army panic, and everyone was afraid. Even General silas admitted with a wry smile: "This is a war between the Roman fleet and Archimedes alone" and "Archimedes is a mythical giant with hundreds of hands".
Edit this personal article.
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, Archimedes was founded.
Some definitions and assumptions, and then proved in turn, as a mathematician, he wrote 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 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, * * * more than 200,000 digits! 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. "circle measurement", using 96 circumscribed circles and inscribed circles, the pi is: 22/7 >; π& gt； 223/7 1, which is the earliest π value in the history of mathematics, clearly points out the error limit. He also proved that the area of a circle is equal to the area of an isosceles triangle with a circumference as the base and a high radius; An exhaustive method was used. "Ball and cylinder", skillfully using the exhaustive method to prove that the surface area of the ball is equal to 4 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". "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. Archimedes
Plane balance is the earliest work of mechanical science, which is about determining the center of gravity of plane and three-dimensional graphics. 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. "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. 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 reduction to absurdity after getting the result.
Edit this scientific achievement.
Geometric aspect
Archimedes determined the area of parabola bow, helix and circle, and the calculation method of 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. Archimedes spiral perpetual motion machine.
astronomy
Archimedes also made outstanding achievements in astronomy. In addition to the planetary instrument mentioned above, he also thinks that the earth is spherical and rotates around the perpetual motion machine together with 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.
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 was an advocate of archimedean spiral's perpetual motion machine.
Automatic manual production of various instruments and machinery. 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. Archimedes invented a cross goniometer for astronomical measurement and made an instrument for measuring the angle between the sun and the earth. His most famous discovery is the principle of buoyancy and relative density, that is, the apparent weight of an object in a liquid is equal to the weight of the liquid, which was later known as Archimedes principle. In geometry, he created a method to find pi, that is, the relationship between the circumference and diameter of a circle. Archimedes was the first engineer to talk about science. In his research, he used Euclid's method, assuming first, and then deducing the result with strict logic. He constantly searched for general principles and applied them to special projects. His works always combine mathematics and physics, so Archimedes became the father of physics. He applied the lever principle to the war, and his deeds of defending silas pigeons are widely known. He also used the same principle to derive the volumes of some spheres and bodies of revolution (ellipsoid, paraboloid of revolution, hyperboloid of revolution). In addition, he also discussed the related principles and achievements of archimedean spiral (such as the trajectory left by flies walking outward from the center of a turntable rotating at a constant speed), circle, ball and cylinder. Archimedes effectively used Euclid's approximation concept. He proposed that a circle circumscribes a polygon, and a similar circle circumscribes a polygon. When the number of sides is large enough, the perimeters of two polygons will approach the circumference of a circle from top to bottom. He used hexagons first, and then doubled the number of sides one by one until he reached 96 polygons. The estimated value of π is between 3. 14 163 and 3. 14286. In addition, he calculated that the surface area of the ball is four times that of the maximum inscribed circle. And he deduced that the volume of a sphere inscribed in a cylinder is two-thirds of that of a cylinder, and this theorem was engraved on his tombstone.
Edit this paragraph: The Death of Archimedes
It is said that when Roman soldiers entered the city, Commander-in-Chief Maceiras, out of admiration for Archimedes' talent, ordered that the saint should not be harmed. Archimedes didn't seem to know that the city had been breached, and he was addicted to mathematics. A Roman soldier suddenly appeared in front of him and ordered him to go to Maceiras. Archimedes sternly refused, so Archimedes unfortunately died by the soldiers' sword. Another way of saying it: Roman soldiers broke into Archimedes' house and saw an old man burying his head in a geometric figure on the ground (another way of saying it is that he was painting on the beach). When the soldiers trampled on the graphics, Archimedes angered the soldiers: "Don't destroy my circle!" " The soldier pulled out his dagger, and the great scientist was killed by the ignorant Roman soldiers. Maceiras was deeply saddened by Archimedes' death. He executed the soldier who killed Archimedes as a murderer and built a mausoleum for Archimedes. According to Archimedes' wishes, the tombstone is engraved with the geometric figure of "cylindrical ball". With the passage of time, Archimedes' mausoleum was drowned by weeds. Later, Cicero, an accountant, politician and philosopher in Sicily (BC 106~ 43), visited Syracuse and found a tombstone engraved with a cylindrical ball in the weeds. Based on this, he recognized this as Archimedes' grave and repaired it.
Edit the tombstone set in this paragraph.
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. On the monument, the figure of the ball carved on the cylinder is carved as a souvenir. Because Archimedes discovered the volume and surface area of the ball, both of which are 2/3 of the volume and surface area of the 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. 100 years later (75 BC), Cicero, a famous Roman politician and writer (106-43 BC). I want to pay my respects to the grave of this great man. However, local residents denied its existence. With the help of a sickle, they found a small pillar that was not much higher than the miscellaneous tree. The spherical and cylindrical patterns engraved on it are impressive. 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. Two thousand years have passed, and with the passage of time, this tomb has disappeared without a trace. Now there is a man. It is about ten meters wide and the inner wall is covered with moss. It is said to be the tomb of Archimedes, but there is no sign to prove its authenticity. Moreover, the news of "finding the real cemetery" has been heard from time to time, and it is difficult to distinguish between true and false.
Edit this paragraph, personal influence.
Archimedes' geometric works are the pinnacle of Greek mathematics. He compared Euclid's strict reasoning method with Plato's transcendental Archimedes.
Rich imaginations are harmoniously combined to reach the realm of perfection and beauty, thus "making the calculus constantly cultivated by Kepler, cavalieri, Fermat, Newton and Leibniz more and more perfect". 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. 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 have played a decisive role in promoting the development of mathematics. 1906, Danish mathematician Heiberg discovered a copy of Archimedes' letter to erato Sese and some other works of Archimedes. Through research, it is found that these letters and transcripts contain the idea of calculus. What he lacks is the concept of no limit, but the essence of his thought extends to the field of infinitesimal analysis, which is maturing in the17th century, and 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.
Editing this passage in Archimedes' sheepskin book
Ancient manuscripts
Archimedes in ancient Greece is the most legendary ancient scientist. Before 1998, Archimedes passed down from generation to generation.
He wrote eight articles, namely: plane balance theory, parabola quadrature, sphere and cylinder, rounding, spiral theory, floating body theory, cone and ellipsoid theory and sand table theory. The contents of these eight articles come from two ancient code systems, which are called "Code A" and "Code B" by experts. Unfortunately, both manuscripts were lost. 1998, an auction called Archimedes sheepskin book appeared at Christie's auction house in new york, which was a humble prayer book copied in the middle ages. But because I believe it was originally a copy of Archimedes' works, it was only later that the handwriting of the original book was scraped off and used to copy prayer books (this kind of "waste utilization" was not uncommon in ancient times), so it was expensive, and it was finally written by a mysterious person. Later, the rich man called himself "Mr. B" and sent someone to find Dr. Noel, director of the manuscript department of Walter Art Museum in Baltimore, and asked Noel to organize a team to study Archimedes' sheepskin book, and the research fund was funded by him. But the sheepskin book should be returned to him after the study. Noel organized a research team including professors of ancient science, history of mathematics, history of medieval art, chemistry, digital imaging, X-ray imaging and ancient manuscripts, all of whom mainly engaged in this research in their spare time on weekends. In the process of research, Mr. B often participates in decision-making. He "has always been responsible, comprehensive and generous." This research team worked hard for seven years-from 1999 to 2006, "this project never lacked funds". The researchers took apart Archimedes' sheepskin book and used various modern imaging techniques, and finally successfully copied the manuscript scraped from parchment more than 700 years ago. So the third Archimedes book handed down from generation to generation reappeared. It is now called "C Codex" and has become the oldest existing copy of Archimedes' works. Codex C includes seven works by Archimedes: Plane Balance, Sphere and Cylinder, Rounding, Spiral, Floating Body, Methodology and Fourteen Tangram. Among them, the first five articles have been handed down by the previous "Code A" and "Code B" systems and are known to the world; The most precious are the last two books, Methodology and Fourteen Tangram, which have never appeared before.
school achievement
During the European Renaissance, the masters at that time devoted themselves to the pursuit of Greek works (even after such heavy translation as Greek-Arabic-Latin). Leonardo da vinci tried his best to search for Archimedes' works, but he couldn't read the methodology, because the Renaissance masters could only rely on "Codex A" and "Codex B" (which had not been lost at that time) to understand Archimedes. And if Leonardo saw the methodology, he would lose his mind-Archimedes' research and achievements greatly surpassed him as early as 1700 years ago. Archimedes has been "very close to modern calculus" in methodology, and there is a profound study of "infinity" in mathematics. What runs through the whole article is how to apply mathematical models in physics. Researchers even think that "Archimedes has the ability to create the kind of physical science created by Galileo and Newton". As for another newly discovered work, Fourteen Tangram, it is quite different. Although the West has long known that the ancient game "Fourteen Tangram" (more complicated than the folk "Tangram" in China), Noel thought that "Fourteen Tangram" was difficult to understand and irrelevant at first, maybe it was just Archimedes' game. But later, after the experts who studied combinatorial mathematics participated in the research, they made an amazing discovery-they thought Archimedes was actually going to discuss the total number * * * How many ways are there to put fourteen puzzles into a square? The answer they studied is: fourteen tangrams can get a square with 17 152 spellings. This makes them believe that the Fourteen Tangram shows that "the Greeks completely mastered the earliest evidence of combinatorial mathematics". The reappearance of Archimedes' two works, Methodology and Fourteen Ingots, provided by Archimedes' sheepskin book can really be said to have "rewritten the history of science".
Edit this famous quote by Archimedes.
First of all, it takes 6 * 10 22 force to lift an object with the same weight as the earth. If the maximum force he can use is 600N, according to the lever balance condition, the power arm should be 22 times of 10 of the resistance arm. Even with such a long lever, there will be no fixed fulcrum relative to the earth in the vast universe, because the stars in the solar system are moving all the time. Even if he finds such a fulcrum, even if he just shakes the earth 1mm, the arc he draws in the universe will reach 10 17 km (about 10000 light years), which is enough for him to play all his life. So up to now, it is impossible for him to pry up the earth just by giving him a direction in the universe. But if you can find a way, it will definitely stir up the world.