Archimedes was born in Syracuse, Sicily, in 287 B.C. He was the son of the astronomer Phidias. Archimedes studied in Alexandria, Egypt, which at the time , was the most important learning center. Humble by nature, he didn’t want glory for his achievements, and to make sure of that, he did not write many of his experiments and mathematical theories. We have some by which the work of future physicist and mathematician was made easier. Archimedes invented the lever, and it was at this occasion that he said:”Give me a place to stand on and I will move the earth”. He was closely associated with Hieron, king of Syracuse, and his son Gelon. For this king Archimedes devised many war machines during the siege of Syracuse by the Romans. By positioning mirrors on the tops of buildings, he was able of burning many ships of the Roman fleet when these came to close to the walls of the city.
On occasion king Hieron charged him to verify if the royal crown that was made for him was of 100% gold. Archimedes thought that if an object was immersed in a liquid, the object should displace so much liquid equal, in weight, to the weight of the object. Archimedes took a piece of gold equal in weight to the weight of the crown: he first immersed the piece of gold in a liquid, and noticed how much liquid had been displaced: it was equal in weight to the weight of the piece of gold. Then he immersed the crown in the liquid, and the liquid displaced was equal in weight to the weight of the crown, but less than the weight of the piece of gold: the crown was not all of gold, it was a mixture of silver and gold.
From this discovery, came the famous Archimedes’ law: A body immersed in a liquid or gas will displace so much liquid equal to the volume of the body immersed. From the same experience came the Archimedes’ principle of buoyancy: A body immersed in a fluid, loses so much weight equal to the weight of the fluid displaced. And: The buoyant force on a body floating in a fluid or gas, is also equivalent in magnitude to the weight of the floating object and is opposite in direction. A break trough in geometry by Archimedes, is the measurement of the “circle”, figuring the value of pi within very narrow limits. At this point Archimedes ran out in the street of the city, shouting: “Eureka!Eureka!” (which means: I found it!) without realizing that he was naked!
Another Archimedes’ invention is the “Water screw” which is still used to-day in Egypt for irrigation purposes. The Water Screw is a corkscrew shaped tube inserted in a water tight cylinder. The tube is immersed in water and by rotating the Screw, water will come out at the other side.
Archimedes died in the capture of Syracuse in 212 B.C. Marcellus, the Roman General, had given order not to kill Archimedes. A soldier, who did not know Archimedes, stabbed him, killing him while he was at work drawing geometrical figures. Marcellus lamented the death of the great inventor, and gave him full honor burial, marking the tomb by a sphere inscribed in a cylinder, as per Archimedes’ desire.
ARCHIMEDES CATTLE PROBLEM
If thou art diligent and wise, o stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacrian isle of Sicily, divided into four herds of different colours, one milk white, another a glossy black, a third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions:
Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all of the yellow.
These were the proportions of the cows: The white were precisely equal to the third part and a fourth of the whole herd of the black; while the black were equal to the fourth part once more of the dappled and with it a fifth part, when all, including the bulls, went to pasture together. Now the dappled in four parts were equal in number to a fifth part and a sixth of the yellow herd.
Finally the yellow were in number equal to a sixth part and a seventh of the white herd. If thou canst accurately tell, o stranger, the number of cattle of the Sun, giving separately the number of well-fed bulls and again the number of females according to each colour, thou wouldst not be called unskilled or ignorant of numbers, but not yet shalt thou be numbered among the wise.
But come, understand also all these conditions regarding the cattle of the Sun. When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth, and the plains of Thrinacia, stretching far in all ways, were filled with their multitude. Again, when the yellow and the dappled bulls were gathered into one herd they stood in such a manner that their number, beginning from one, grew slowly greater till it completed a triangular figure, there being no bulls of other colours in their midst nor none of them lacking.
If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.