Archimedes

Archimedes

Was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.

When the Romans had arrived before the city, Archimedes was leading the defense. Polybius, Titus Livius and Plutarch described the means that the genius of Archimedes used in these circumstances to cause damage to the enemy vessels. For three years, the science of one man held up Marcellus’ army. He built machines capable of throwing arrows at considerable distances. He built long beams, outside the walls, that could throw very large weights at the enemy ships and with the help of them he could hook the ships to catch them, to raise them and then to throw them, submerging them. He invented mirrors that burned the enemy ships by the sunlight concentration.

One of the most important theoretical works of Archimedes is titled: “On the equilibrium of planes” and has two parts. In the first part, Archimedes laid the foundations of a new science, statics, a branch of mechanics, and treats in its content the matter of levers and the center of gravity. Of course, levers were known for a long time and used by people. Archimedes didn’t discover the use of levers, but he discovered the mathematical laws of levers. The extraordinary significance of the leveraging laws is rendered expressively with the words transmitted through the legend: “Give me a fulcrum and I will capsize the Earth!”, impressive words, that Archimedes might have said when he explained the importance of this law.

Legend has it that Archimedes, found the solution while being in the bathroom. He would have jumped up shouting loud “Eureka”, which means “I found it”. He then discovered the law which is now named after him: a body immersed in a fluid is pushed from the bottom to the surface with a force equal to the weight of the displaced liquid.

He wrote a work of architecture entitled “The Sand Reckoner”, another one of geometry “On Conoids and Spheroids” and another important one entitled “The Quadrature of the Parabola”. From Archimedes we have learned to measure the length of the circle and to calculate the value of π (Pi). He also studied special curves called spirals, today called Archimedes spiral.

Archimedes’ “Book of Lemmas” or “Liber Assumptorum” is a treatise with 15 propositions on the nature of circles. The earliest known copy of the text is in Arabic. The Lemmas may be based on an earlier work by Archimedes that is now lost. It has also been claimed that Heron’s formula for calculating the area of a triangle from the length of its sides was known to Archimedes. However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century AD.

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