Archimede (Archimedes)

The details of Archimedes's life are obscure; a biography of Archimedes mentioned by Eutocius was allegedly written by his friend Heraclides Lembus, but this work has been lost, and modern scholarship is doubtful that it was written by Heraclides to begin with.
Based on a statement by the Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC, Archimedes is estimated to have been born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known; Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse, although Cicero and Silius Italicus suggest he was of humble origin. It is also unknown whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth; though his surviving written works, addressed to Dositheus of Pelusium, a student of the Alexandrian astronomer Conon of Samos, and to the head librarian Eratosthenes of Cyrene, suggested that he maintained collegial relations with scholars based there. In the preface to On Spirals addressed to Dositheus, Archimedes says that "many years have elapsed since Conon's death." Conon of Samos lived c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works.

Golden wreath

Another story of a problem that Archimedes is credited solving with in service of Hiero II is the "wreath problem." According to Vitruvius, writing about two centuries after Archimedes' death, King Hiero II of Syracuse had commissioned a golden wreath for a temple to the immortal gods, and had supplied pure gold to be used by the…

While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics, both in applying the techniques of his predecessors to obtain new results, and developing new methods of his own.

Method of exhaustion

In Quadrature of the Parabola, Archimedes states that a certain proposition in Euclid's Elements demonstrating that the area of a circle is proportional to its diameter was proven using a lemma now known as the Archimedean property, that “the excess by which the greater of two unequal regions exceed the lesser, if added to itself, can exceed any given bounded region.” Prior to Archimedes, Eudoxus of Cnidus and other earlier mathematicians applied this lemma, a technique now referred to as the "method of exhaustion," to find the volume of a tetrahedron, cylinder, cone, and sphere, for which proofs are given in book XII of Euclid's Elements.
In Measurement of a Circle, Archimedes employed this method to show that the area of a circle is the same as a right triangle whose base and height are equal to its radius and circumference. He then approximated the ratio between the radius and the circumference, the value of π, by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of a circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 3⁠1/7⁠ (approx. 3.1429) and 3⁠10/71⁠ (approx. 3.1408), consistent with its actual value of approximately 3.1416. In the same treatise, he also asserts that the…

Archimedes made his work known through correspondence with mathematicians in Alexandria, which were originally written in Doric Greek, the dialect of ancient Syracuse.

Surviving works
The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986).

Measurement of a Circle

This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes gives an approximation of the value of pi (π), showing that it is greater than ⁠223/71⁠ (3.1408...) and less than ⁠22/7⁠ (3.1428...).

The Sand Reckoner

In this treatise, also known as Psammites, Archimedes finds a number that is greater than the grains of sand needed to fill the universe. This book mentions the heliocentric theory of the Solar System proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies, and attempts to measure the apparent diameter of the Sun. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner is the only surviving work in which Archimedes discusses his views on astronomy.
Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as Aristarchus' heliocentric model of the universe, in the Sand-Reckoner. Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations…

Sometimes called the father of mathematics and mathematical physics, historians of science and mathematics almost universally agree that Archimedes was the finest mathematician from antiquity.

Classical antiquity
The reputation that Archimedes had for mechanical inventions in classical antiquity is well-documented; Athenaeus recounts in his Deipnosophistae how Archimedes launched the largest known ship in antiquity, the Syracusia, while Apuleius talks about his work in catoptrics. Plutarch had claimed that Archimedes disdained mechanics and focused primarily on pure geometry, but this is generally considered to be a mischaracterization by modern scholarship, fabricated to bolster Plutarch's own Platonist values rather than to an accurate presentation of Archimedes.

Middle ages

Archimedes' work was translated into Arabic by Thābit ibn Qurra, and into Latin via Arabic by Gerard of Cremona. Direct Greek to Latin translations were later done by William of Moerbeke and Iacobus Cremonensis.

Renaissance and early modern Europe

During the Renaissance, the Editio princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin, which were an influential source of ideas for scientists during the Renaissance and again in the 17th century.
Leonardo da Vinci repeatedly expressed admiration for Archimedes, and attributed his invention Architonnerre to Archimedes. Galileo Galilei called him "superhuman" and "my master", while Christiaan Huygens said, "I think Archimedes is comparable to no one", consciously emulating him in his early work. Gottfried Wilhelm Leibniz said, "He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times".
Italian numismatist and…