Information on the mathematician Archimedes, what are Archimedes achievements in mathematics?

Archimedes determined the area of parabolic bows, spirals, circles, and the surface area and volume of various complex geometries such as ellipsoids and paraboloids. In the process of deriving these formulas, he created the "exhaustion method", which we today call a step-by-step approximation of the limit, and is therefore recognized as the originator of calculus calculations. He used the method of increasing the number of sides of the inner and outer polygons of the circle and gradually approaching the area, and found the pi more accurately.

In the face of the cumbersome numerical representation in ancient Greece, Archimedes also pioneered the method of remembering large numbers, breaking through the limitation that the Greek alphabet could not be counted more than 10,000 at that time, and used it to solve many mathematical problems.

1. The short story of Chen Jingrun in mathematics.

Mathematician Chen Jingrun, while thinking about a problem, walked and hit the trunk of a tree without raising his head and said, "I'm sorry, I'm sorry." "Keep thinking.

2. The short story of the mathematician Rudolph.

In the 16th century, the German mathematician Rudolph spent his whole life calculating pi to 35 decimal places, which later generations called Rudolph's number, and after his death, others engraved this number on his tombstone.

3. The short story of the mathematician Jacob Bernoulli.

After his death, the Swiss mathematician Jacob Bernoulli, who studied the spiral (known as the line of life), was engraved on his tombstone with a logarithmic spiral, and the inscription reads: "Although I have changed, I am the same." It's a pun that both portrays the nature of the spiral and symbolizes his love for mathematics.

4. The ancient Greek scholar Archimedes died at the hands of the Roman enemy soldiers who attacked Sicily (before his death he was still in the Lord: "Don't break my circle.") Later, in his tombstone, a figure of a ball cut into a cylinder was engraved on his tombstone to commemorate his discovery that the volume and surface area of the ball were two-thirds of the volume and surface area of the cylinder.

5. Archimedes was born in 287 BC in Syracuse, Sicily, at the southern tip of the Italian peninsula. His father was a mathematician and astronomer. Archimedes had a good family upbringing from an early age, and at the age of 11 he was sent to Alexandria, the center of Greek culture at the time, to study.

In this called"The capital of wisdom"In the famous city, Archimedes read a lot of books, absorbed a lot of knowledge from the bright sky, and became a disciple of Euclid's pupils Eratose and Canon, and studied the "Geometric Primitive".

Archimedes (287 B.C. - 212 B.C.), a great ancient Greek philosopher, encyclopedic scientist, mathematician, physicist, mechanic, founder of static mechanics and hydrostatics, and enjoys the reputation of "father of mechanics", Archimedes and Gauss, Newton are listed as the world's three major mathematicians. Archimedes once said, "Give me a fulcrum, and I will pry up the whole earth."

> Archimedes established the basic principles of statics and hydrostatics. A number of methods are given for finding the center of gravity of a geometric figure, including the center of gravity of the figure enclosed by a parabola and its parallel chords. Archimedes proved that the buoyancy of an object in a liquid body is equal to the weight of the liquid it distributes, a result that became known as Archimedes' principle.

He also gave the criterion that the positive parabolic rotating body floats in a liquid and is balanced and stable. Archimedes' invented machinery includes a water spiral for water diversion, a lever pulley machine that can pull a fully loaded ship, and an earth-moon-sun model that can explain the phenomenon of solar and lunar eclipses. However, he did not write about mechanical inventions because he considered them inferior to pure mathematics.

Archimedes also used the method of continuous segmentation to find the volume of ellipsoids, rotating projectiles, etc., which already had the rudiments of integral calculation.

was a great ancient Greek philosopherArchimedes

He was not only a philosopher, but also an encyclopedic scientist, a mathician, a physicist, a mechanic, the founder of static mechanics and hydrostatics, and was known as the "father of mechanics".

Archimedes, Gauss and Newton are the world's top three mathematicians.

His teacher was Euclid.

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His main achievements are:

The principle of buoyancy

Brief description of the principle of buoyancy: the buoyancy obtained by an object in a liquid is equal to the weight of the liquid it discharges, that is: f=g (where f is the buoyancy force of the object, and g is the gravitational force of the object to displace the liquid). The deformation of this formula can be obtained.

where is the density of the liquid being discharged, g is the acceleration due to local gravity, and v is the volume of the liquid being discharged).

Leverage principle

Lever principle: The system that satisfies the following three points is basically leverage: fulcrum, force point, and force point.

The principle of leverage is also known as the "lever equilibrium condition": for a lever to be balanced, the two moments acting on the lever (the product of the force and the arm of the force) must be of equal magnitude. Namely:

Power Power Arm = Resistance Resistance Arm, which can be expressed by the formula as:

F1 represents power, L1 represents power arm, F2 represents resistance, and L2 represents resistance arm).

Mechanical applications

Archimedes' research on machinery originated from his study in Alexandria, one day Archimedes was walking by the Nile River for a long time, and saw that the peasants were laborious to carry water and irrigate the land. In Egypt, until modern times 2,000 years later, people still used this device. This tool became the ancestor of the later screw thruster.

Archimedes attached great importance to experimentation, and designed and manufactured many instruments and machinery throughout his life, including weightlifting pulleys, irrigators, water lifters, mountain friend keys, and military stone throwing machines.

Archimedes also had brilliant achievements in mathematics and became a great mathematician during the Alexandrian period. His greatest contribution to mathematics was the study of geometry. In the book "The Measurement of Circles", he proved that pi is between and ; He also developed the exhaustion method of his predecessors, which was used to find area and volume, and found the formula for the surface area and volume of spheres, cylinders, ellipsoids, and cones.

Archimedes was an ancient Greek mathematician and mechanic. Born in Syracuse, Sicily, circa 287 BC; He died in Syracuse c. 212 BC. Archimedes' geometric writings were the pinnacle of Greek mathematics.

He harmoniously combined Euclid's rigorous method of reasoning with Plato's a priori rich imagination to achieve the ultimate perfection, thus "perfecting the calculus that Kepler, Cavalieri, Fermat, Newton, Leibniz, and others continued to cultivate." Archimedes was also the greatest mechanic of ancient Greece. He discovered the law of buoyancy, the principle of leverage, about which he once proudly said:

Give me a fulcrum and I will be able to move the earth".