To Lesson 4 Archimedes

Archimedes was born in 287 ВС in Syracuse, Sicily and died in 212 ВС in Syracuse, Sicily.

Archimedes’ father was Phidias, an astronomer. We know nothing else about Phidias other than this one fact and we only know this since Archimedes gives us this information in one of his works, The Sandreckoner. A friend of Archimedes called Heraclites wrote a biography of him but sadly this work is lost.

Archimedes was a native of Syracuse, Sicily. It is reported by some authors that he visited Egypt and there invented a device now known as Archimedes’ screw. This is a pump, still used in many parts of the world. When he was a young man, Archimedes studied with the successors of Euclid in Alexandria. Certainly he was completely familiar with the mathematics developed there, but what makes this version much more certain, he knew personally the mathematicians working there and he sent his results to Alexandria with personal messages!

Yet Archimedes, although he achieved fame by his mechanical inventions, believed that pure mathematics was the only worthy matter.

The achievements of Archimedes are quite outstanding. He is considered by most historians of mathematics as one of the greatest mathematicians of all times. He perfected a method of integration which allowed him to find areas, volumes and surface areas of many bodies.

Archimedes was able to apply the method of exhaustion (метод перебора), which is the early form of integration, to obtain a whole range of important results. Archimedes also showed that he could approximate square roots accurately. He invented a system for expressing large numbers. In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids. His most famous theorem gives the weight of a body immersed in a liquid, called Archimedes’ principle. This principle is contained in his work On floating bodies, a work in which Archimedes lays down the basic principles of hydrostatics. He also studied the stability of various floating bodies of different shapes and different specific gravities.

The Sandreckoner is a remarkable work in which Archimedes proposes a number system capable of expressing numbers up to 8*10⁶³ in modem notation. He argues in this work that this number is large enough to count the number of grains of sand which could be fitted into the universe.

Archimedes was killed in 212 ВС during the capture of Syracuse by the Romans in the Second Punic War after all his efforts to hold back the Romans with his machines of war had failed.

Albert Einstein

Albert Einstein was born in Germany in 1879. He enjoyed classical music and played the violin. One story Einstein liked to tell about his childhood was of a wonder he saw when he was four or five years old: a magnetic compass. The needle’s invariable northward swing, guided by an invisible force, profoundly impressed the child. The compass convinced him that there had to be “something behind things, something deeply hidden”.

Even as a small boy Albert Einstein was self-sufficient and thoughtful. According to family legend he was a slow talker, pausing to consider what he would say. His sister remembered the concentration and perseverance with which he would build houses of cards.

Albert Einstein’s first job was that of patent clerk.

In 1933, he joined the staff of the newly created Institute for Advanced Study in Princeton, New Jersey. He accepted this position for life, living there until his death. Einstein is probably familiar to most people for his mathematical equation about the nature of energy, E= MC².

Albert Einstein wrote a paper with a new understanding of the structure of light. He argued that light can act as though it consists of discrete, independent particles of energy, in some ways like the particles of a gas. A few years before, Max Planck’s work had contained the first suggestion of discreteness in energy, but Einstein went far beyond this. His revolutionary idea seemed to contradict the universally accepted theory that light consists of smoothly oscillating electromagnetic waves. But Einstein showed that light quanta, as he called the particles of energy, could help to explain phenomena being studied by experimental physicists. For example, he made clear how light ejects electrons from metals.

There was a well-known kinetic energy theory that explained heat as an effect of the ceaseless motion of atoms; Einstein proposed a way to put the theory to a new and crucial experimental test. If tiny but visible particles were suspended in a liquid, he said, the irregular bombardment by the liquid’s invisible atoms should cause the suspended particles to carry out a random jittering dance. One should be able to observe this through a microscope, and if the predicted motion were not seen, the whole kinetic theory would be in grave danger. But just such a random dance of microscopic particles had long since been observed. Now the motion was explained in detail. Albert Einstein had reinforced the kinetic theory, and he had created a powerful new tool for studying the movement of atoms.

Einstein’s researches are, of course, well chronicled and his more important works include Special Theory of Relativity (1905), Relativity (English translations, 1920 and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) are perhaps the most important.

Albert Einstein received honorary doctorate degrees in science, medicine and philosophy from many European and American universities. During the 1920’s he lectured in Europe, America and the Far East and he was awarded Fellowships or Memberships of all the leading scientific academies throughout the world. He gained numerous awards in recognition of his work, including the Copley Medal of the Royal Society of London in 1925, and the Franklin Medal of the Franklin Institute in 1935.

Einstein’s gifts inevitably resulted in his dwelling much in intellectual solitude. Music played an important role in his life. He married Mileva Marie in 1903 and they had a daughter and two sons; their marriage was dissolved in 1919 and that very year he married his cousin, Elsa Lowenthal, who died in 1936. He died on April 18, 1955 at Princeton, New Jersey.