Archimedes' study of machinery originated from his study in Alexandria. One day after a long drought, Archimedes was walking along the Nile. He saw a farmer saying.

Archimedes

Irrigation of the land is quite laborious. He thought about it and invented a tool to suck up water by rotating in a water pipe through a spiral action. Later people called it "Archimedes spiral water lifter", which 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. He is more interested and spends more time 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

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.

Astronomy:

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".

personal work

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 curved graphics.

Complete works of Archimedes

The style of product and volume of curved cube is deeply influenced by Euclid's Elements of Geometry. Firstly, some definitions and assumptions are established, and then it is proved in turn that as a mathematician, he has written 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, exceeding 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.

In the measurement of a circle, using the circumscribed circle and the inscribed 96-sided circle, the pi is 22/7.