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Personality: The genius of Archimedes
It is important to be familiar with the achievements of the eminent scientists of the past. Archimedes (287 BC — 212 BC) enjoys a prominent position among those who contributed towards shaping our lives in this world.
One of the most important discoveries made by Archimedes was the concept of specific gravity, which ultimately led to the invention of the ship. He, thus, provided a source of water navigation.
It is said that Hieron II, the king of Syracuse, had given a certain amount of gold to his jeweller to be moulded into a crown. When the jeweller presented the crown to the king, Hieron suspected that the jeweller might have replaced some gold with an equal amount of silver.
History has yet to witness a more dedicated mathematician than Archimedes. The discipline owes a great deal to him.
Hence, the crown had to be tested for purity. Accordingly, he commissioned his court scientist, Archimedes, to detect if there was any fraud involved.
After many days of fruitless research, Archimedes was about to abandon the task. But one morning, as he stepped into the tub at a public bathhouse, he noticed how it had overflowed when he stepped in. The flow of water triggered his imagination, and he realized that the amount of displaced water must be exactly the same volume as himself.
He leapt out of the tub and ran home through the streets of Syracuse crying, “Eureka! Eureka! I have found it! I have found it!”
What he had found was a simple solution to Hieron’s problem. After a few experiments, Archimedes determined the quantity of displaced water. He found that the amount of water displaced by the crown was more than the amount of displaced water by gold. This provided the world with the most profound mysteries of specific gravity of different substances.
The law of specific gravity is known as the “Principle of Archimedes” and may be stated as: “A body immersed in fluid loses as much in weight as the weight of an equal volume of fluid.” Geometry and mathematics were the pastime of Archimedes and he used to make geometric figures with his fingers. Archimedes was fortunate that during his time, the two disciplines flourished a great deal.
The father of geometry, Euclid, belonged to the same age. Archimedes was the pupil of Canon. The three belonged to the University of Alexandria, a seat of high learning at the time.
As a young man, Archimedes continued the study of geometry from the point where Euclid had left off. He calculated the ratio of circumference using the diameter of a circle. He also discovered the method of measuring the areas and the volumes of circular and spherical objects.
One of his other contributions is finding the relationship between the volume of a cylinder and that of an inscribed ball, where the volume of an inscribed sphere is equal to exactly two-thirds of the volume of the enclosing cylinder.
Archimedes was so proud of this discovery that he ordered the figure of a sphere within a cylinder to be carved upon his tombstone.
In spite of his dislike for royalty, Archimedes was forced to work for king Hieron and, therefore, felt obliged as a subject and as a kinsman to obey his orders. Working under royal orders, the scientist was responsible for no less than forty inventions. Some of these were for commercial use, but most of them were for military purposes.
Perhaps the most interesting of his commercial inventions was the so-called “Screw of Archimedes”. The hollow screw is placed on an inclined surface with the lower end immersed in a pool of water. When the spiral turning constantly from left to right scoops up, the water at the bottom would spill out at the top. This commercial invention was so useful that it was employed for a very long time for draining swamps in large areas.
When Syracuse, Archimedes’s native city, was attacked by Romans, Hieron called him to device new weapons against the siege. A Roman fleet under the leadership of Marcellus had set out against Syracuse.
In order to stall the fleet, Archimedes came up with the idea of ‘burning mirrors’. He made the required preparations, and as soon as the enemy ships came within range, the trained battery of huge concave mirrors was turned on.
These mirrors were made of highly reflective metal plates designed to focus the blazing light on the oncoming fleet. It is interesting to note that Sir Isaac Newton, after a series of experiments with concave mirrors, expressed his opinion that such an invention on the part of Archimedes was not beyond the scope of scientific possibilities.
When the siege of Syracuse became a serious threat, Hieron once again called the scientist to his aid. The king wanted Archimedes to drown the ships altogether.
This time he came up with the theory of livers and pulleys, by which he could move maximum weight by a minimum of effort. When Hieron expressed his doubts about the efficacy of the plan, Archimedes proceeded to put it to the trial.
He constructed multiple pulleys, attached the chain of one end of a pulley to a large and laden Syracuse ship, and handed the rope on the other end to Hieron. The king was then asked to pull. The king pulled the rope and saw the ship lifting.
The Roman commanders had reached the wall of Syracuse, equipped with a fleet of 60 vessels loaded with all sorts of arms and missiles. But all of this just proved to be a handful of toys in the enormous iron-grappling hooks which were attached to the pulleys set up by Archimedes.
Descending on the Roman ships like birds of prey, these iron claws drew them up in the air and then plunged them into the sea’s depths. When Marcellus saw the devastation of his fleet, he became fearful and ordered the war to be stopped. Finally, the Roman soldiers became too scared to advance and fled.
Realizing the impossibility of conquest by assault, Marcellus had decided to overcome Syracusans by means of a siege. Yet in spite of this blockade, Archimedes’s ingenuity held off a surrender for three years. And even then it was through the carelessness of Syracusans that their city fell.
It was the night of the festival held in honour of Artemis, the goddess of moon. The people of the beleaguered city had yielded themselves up too frequently to wine and sports. Shortly before dawn, when their senses were befuddled and bodies worn out, a number of Roman soldiers succeeded in scaling the walls and in opening the gates from within.
As for Archimedes, he was sitting in the marketplace, drawing a circle in the sand and calculating, when the Romans came. So absorbed was he that when he saw a drunken Roman soldier rush towards him with his sword, he said: “Before you kill me, my friend, let me finish my circle”. But the soldier gave no heed and killed him, without realizing that he had destroyed an asset.
The writer is a former senior scientific officer of the PCSIR Laboratory
The legacy of a legendIn the very long line of Greek mathematicians from Thales of Miletus and Pythagoras to Pappus of Alexandria in the fourth century AD, Archimedes is the undisputed leading figure.
Although his main claim to fame is as a mathematician, Archimedes is also known for his many discoveries and inventions in physics and engineering, which include the following:
Water screw — His invention of the water screw is still in use in Egypt for irrigation, draining marshy land, and pumping out water from the bilges of ships.
Burning mirror and pulleys — Various devices which he invented were used in defending Syracuse when it was besieged by the Romans. These include powerful catapults, the burning mirror and systems of pulleys.
It was his pride in what he could lift with the aid of pulleys and levers which provoked his glorious hyperbole “Give me a place to stand and I will move the Earth”.
Hydrostatic principal — He discovered the hydrostatic principle which holds that a body immersed in a fluid is subject to an upthrust equal to the weight of fluid displaced by it.
Here is a brief description of the other significant contributions which Archimedes made to mathematics.
Area of parabola — He computed the area of a segment of a parabola. He used a most ingenious argument involving the construction of an infinite number of inscribed triangles which “exhausted” the area of the parabolic segment.
Area of an eclipse — He computed the area of an ellipse by essentially “squashing” a circle.
Volume and surface area of sphere — He found the volume and surface area of a sphere. Archimedes gave instructions that his tombstone should have on it a diagram consisting of a sphere with a circumscribing cylinder.
C.H. Edwards writes how Cicero, while serving in Sicily, had Archimedes’ tombstone restored, and adds: “The Romans had so little interest in pure mathematics that this action by Cicero was probably the greatest single contribution of any Roman to the history of mathematics.”
The Archimedes spiral — He discussed properties of the “Archimedean spiral”, which is defined as follows: the distance from a fixed point O of any point P on the spiral is proportional to the angle between OP and a fixed line through O.
In his evaluation of areas involving the spiral he anticipated methods of the calculus which were not developed until the 17th century AD.
Solids of revolution — He found the volumes of various “solids of revolution” obtained by rotating a curve about a fixed straight line.— http://www-maths.mcs.st-andrews.ac.uk/
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