Archimedes (c. 287 BC, Siracusa - c. 212 BC Siracusa), Ancient Greek mathematician, physicist, astronomer, philosopher and engineer.

He is considered the first and greatest scientist of the ancient world. He laid the foundations of hydrostatics and mechanics.

The buoyant force of water claimed to be found while bathing in a bath is his best known contribution to science. This force is equal to the product of the sinking volume of the object, the density of the liquid it is in, and the gravitational acceleration. Also, according to many mathematical historians, Archimedes is the source of integral calculus.

Archimedes was born around 287 BC in the port city of Syracuse. At that time, Syracuse was an autonomous colony of Magna Graecia. The date of birth is based on the statement of the Greek historian Ioannes Tzetzes that Archimedes lived 75 years. In The Sand Counter, Archimedes says that his father's name is Phidias. There is no known information about his father, an astronomer. In Plutarhos Parallel Lives, Archimedes Syracuse ruler King II. He writes that he is related to Hiero. [3] A biography of Archimedes was written by his friend Heracleides, but this work has been lost. The disappearance of this work left the details of his life unclear. For example, it is not known whether she was married or had children. He may have studied in Alexandria, where his contemporaries Eratosthenes and Konon were in his youth. He mentions Konon as his friend and addresses the beginning of his two works (The Method of Mechanical Theorems and the Bovine Problem) to Eratosthenes.

Archimedes died around 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year siege. According to the popular legend told by Plutarhos, Archimedes was designing a mathematical diagram when the city was captured. A Roman soldier ordered him to come and meet General Marcellus, but Archimedes refused the offer, saying he should finish working on the problem. The soldier was enraged by this and killed Archimedes with his sword. In addition, Plutarhos has a lesser known account of Archimedes' death. This rumor suggests that a Roman soldier might have been killed while trying to surrender. According to the story, Archimedes was carrying mathematical tools. The soldier thought the tools could be valuable items and killed Archimedes. General Marcellus was reportedly outraged at Archimedes' death. The general thought Archimedes was a valuable scientific asset and gave orders not to be harmed. Marcellus refers to Archimedes as "a geometric Briareus."

The last word attributed to Archimedes is "Do not break my circles", allegedly meant to be disturbed by the Roman soldier while working on the circles in the mathematical drawing. This quote is often referred to as "Noli turbare circulos meos" in Latin. However, there is no reliable evidence that Archimedes said these words, and neither is there in the rumor told by Plutarhos. Valerius Maximus in his Unforgettable Works and Words of the 1st century AD stated the phrase “… sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'” - “… but protecting the dust with his hands 'I beg you, do not spoil it.' he said ”. This expression is also used in Katarevusa Greek "μὴ μου τοὺς κύκλους τάραττε!" Expressed as (Mē mou tous kuklous taratte!).

Archimedes has a sculpture in his tomb showing a drawing of his favorite mathematical proof. This drawing consists of a sphere and a cylinder of the same height and diameter. Archimedes proved that the volume and surface area of the sphere equal two thirds of the cylinder, including its bases. In 75 BC, 137 years after Archimedes' death, the Roman orator Cicero was working as a quaestor in Sicily. He had heard the stories of Archimedes' tomb, but none of the locals could show him the place. He eventually found the tomb in a neglected condition and among the bushes next to the Agrigentine gate in Syracuse. Cicero had the grave cleared. After cleaning, he was now able to see the carving and read the strings attached as inscriptions. In the early 1960s, a tomb was found in the courtyard of Hotel Panorama in Siracusa, and it was claimed to be Archimedes' tomb. However, there was no convincing evidence to make this claim true. The current location of his grave is unknown.

Standard versions of Archimedes life were written by Ancient Roman historians long after his death. The siege of Syracuse, narrated in Polibios's History, was written about seventy years after Archimedes' death and was later used as a source by Plutarch and Titus Livius. Focusing on the war machines that Archimedes are said to have built to defend the city, this work gives little information about Archimedes' personality.

Inventions

Mechanical

Archimedes' inventions in the field of mechanics include compound pulleys, endless screws, hydraulic screws, and burning mirrors, so much so that Archimedes burned Roman ships with mirrors. No works related to these were given, but left many works that made significant contributions to the field of geometry of mathematics, static and hydrostatic fields of physics.

The scientist who first revealed the principles of balance is Archimedes. Some of these principles are:

Equal weights suspended on equal arms remain balanced. Unequal weights remain in equilibrium on unequal arms when the following condition is met: f1 • a = f2 • b Based on his work, he said "Give me a fulcrum, let me move the Earth." word has not dropped from languages for centuries.

Geometry

One of his most important contributions to geometry is that he proves that a sphere has a surface area equal to 4 (\ displaystyle \ pi) \ pir2 and its volume is equal to 4/3 (\ displaystyle \ pi) \ pir3. He proved that the area of a circle is equal to the area of a triangle whose base is equal to the circumference of this circle and the height is equal to the radius, and showed that the value of pi lies between 3 + 7/3 and 10 + 71/XNUMX. In other words, these formulas are the diameter of the mass that water can take during volume usage.

Mathematics

One of Archimedes' brilliant mathematical achievements was that he developed some methods for finding the areas of curved surfaces. He approached the infinitesimal calculus while rectangularing a parabola cut. The infinitesimal calculus is the ability to mathematically add an even smaller part than the smallest part imaginable to an area. This account has an enormous historical value. It later formed the basis for the development of modern mathematics, providing a good basis for the differential equations and integral calculus discovered by Newton and Leibniz. Archimedes, in his book Quadrangulating the Parabola, proved that the area of a parabola cut by the consumption method is equal to 4/3 of the area of a triangle with the same base and height.

Hydrostatic

Archimedes also found the "law of balance of liquids" known by his name. The best known story about an object immersed in water is that it loses its own weight as much as the water it carries, and shouts out of the bathhouse “eureka” (I found it), naked, naked. It is rumored that one day, King Hieron II suspected that the goldsmith had mixed silver into the golden crown he had made and referred the solution to this problem to Archimedes. Archimedes, who could not solve the problem, although he thought a lot, felt that when he went to a bath to wash, his weight decreased while he was in the bath pool and jumped out of the bath by saying “evreka, evreka”. What Archimedes found; It was the solution of the problem by comparing the water carried by the gold given for the crown and the water carried by the crown. Because the specific gravity of each substance is different, different objects with the same weight have different volumes. For this reason, two different objects of the same weight immersed in water carry different amounts of water.

works

Most of Archimedes' works are in the form of correspondence with famous mathematicians of the period such as Konon from Samos (Samos) and Erastosthenes of Kirenes, and they are completely theoretical. Greek originals of nine of his works have survived to this day. His works remained in the dark for many years; His contribution to mathematics was not realized until his works were translated into Arabic in the 8th or 9th century. For example, one of Archimedes' very important work titled “Method”, written in order to contribute to other mathematicians, remained in the dark until the 19th century.

On balance (2 volumes). The main principles of mechanics are explained with geometry methods.
Second Order Parabolas
On Sphere and Cylinder Surface (2 volumes). He gave information about the area of a part of a sphere, the area of a circle, the area of the cylinder, and the comparison of the areas of these objects.
On the Spirals. Archimedes defined the spiral in this work, examined the lengths and angles of the radius vector of the spiral, and calculated the tangent of the vector.
On Conoids
On Floating Bodies (2 volumes). The basic principles of hydrostatics are given.
Measuring the Circle
Sandreckone. It includes the system that Archimedes wrote on number systems and created to express large numbers.
Method of Mechanical Theorems. It was found by the famous linguist Heiberg in 1906 among old scrolls (engraved and then rewritten) in Istanbul.

Who is Archimedes?