# Archimedes

Archimedes Thoughtful by Fetti (1620)

When we think of the great scientists and mathematicians of the ancient world, who have contributed greatly to today's inventions and researches, who could forget Archimedes.

In the hearts and minds of scientists Archimedes occupies the same respectable position as Newton and Gauss. In his ancient Greek days he was known as the "the wise one," "the master" and "the great geometer". His works such as the "Death Ray" gained him popularity and fame that lasts till this day. He was one of the last great Greek mathematicians.

**Biography**

Archimedes was born in 287 B.C. in the port of Syracuse, Sicily in the colony of Magna Graecia. His father was Phidias, who was an astronomer about whom nothing is known. We derive this information about Archimedes from his work "The Sand Reckoner".

In those times, in the absence of paper or blackboards, Archimedes used dust, ashes or any other available surface to draw his geometric figures. He used to get so engrossed in his work that sometimes he forgot to eat. It is alleged that he drew figures on his body after bathing and applying olive oil. According to the Greek historian John Tzetzes, who was famous for his research on Byzantinne Greek era, Archimedes lived for 75 years.

Except for the period of his life where he attended school in Alexandria at Euclid's, Archimedes spent all his life at Syracuse. Ancient Greek biographer Plutarch, relates Archimedes to King Hiero II of Syracuse. He says Archimedes achieved so much fame because of his relation to King Hiero II and Gelon (son of King Hiero II). He was a close friend of Gelon and helped Hiero solve complex problem with extreme ease, utterly amazing his friend.

Archimedes died in 212 B.C. during the Second Punic war, when Syracuse was captured by the Roman forces after a two year siege.

According to Plutarch, Archimedes was researching a mathematical diagram, when a Roman soldier ordered him to meet General Marcus (who was engaged in the siege of Syracuse). But Archimedes declined saying that he had to finish his diagram. Furious, the Roman soldier killed Archimedes. General Marcus was angered by the death of Archimedes, because he didn't wish him any harm. Another popular theory regarding Archimedes' death is that he was killed while actually surrendering to the Romans.

**Tomb of Archimedes**

The tomb of Archimedes is famous for it depicts his famous diagram, a sphere in a cylinder of the exact height and diameter. Archimedes had earlier proved that the volume and surface area of the sphere would be two thirds that of the cylinder. In 75 B.C., 137 years after the death of Archimedes, it was Cicero who was responsible for giving respect and attention to Archimedes' tomb, which had been long neglected. Cicero had heard about the tomb of Archimedes, but it took him a long time to find it, as the local populace were unable to help. Ultimately he found it at the Agrigentine gate in Syracuse, covered in bushes. He cleaned up the tomb and gave it its due respect.

**Discoveries and Inventions**

Archimedes has many discoveries and inventions to his credit, but he considered his theoretical work as his main triumph. Along with his inventions in mathematics and geometry, he is also known for the weapons he created for King Hiero II to help protect Syracuse. He is credited with many inventions in the field of mathematics and physics such as "Death ray", "Archimedes claw", hydrostatics, calculus, etc.. Some of his discoveries are stated below:

**Hydrostatics:**

Today when we get any idea, we often shout the word 'Eureka'. This famous word is originally attributed to Archimedes, for the invention of measuring the volume of an object with an irregular shape. Once when Hiero had ordered a gold crown, he suspected that the crown was not made of pure gold but also silver. However, he could not prove this. He told Archimedes of his suspicion.

One day as Archimedes thoughts were revolving around the problem, he took a bath in his bathtub. He realized that the amount of water that overflowed the tub was proportional to the amount of his body that was submerged. At the realization he came shouting out of the bathtub "Eureka, Eureka" and ran out on to the streets of Syracuse completely naked.

In his work 'The Floating Bodies', this principle is known as the 'Archimedes Principle'. But the example of golden crown does not appear in any known works of Archimedes.

**Principle of levers:**

Although Archimedes did not invent the lever, he discovered the reasoning behind why it worked. It is said that he remarked, "Give me a place to stand on, and I will move the Earth." Plutarch explained how Archimedes designed the block and tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to shift. It is also said that Archimedes built the Syracusia ship, which was the largest vessel of its time and capable of transporting 600 passengers. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes' screw was purportedly developed in order to remove the bilge water. The screw was a machine with a revolving screw shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals.

**Archimedes' claw:**

Archimedes' claw was invented to defend the city of Syracuse. Known as the 'ship-shaker', it is shaped like a crane arm, from which a large metal hook was balanced. When the claw was dropped on an attacking ship, it would lift the ship by swinging the arm upwards and then sink the ship.

**Death Ray:**

There have bee n many doubts about Archimedes weapon of the death Ray. However in 2005 the Death Ray was proved and tested by a University class (MIT). Using over one hundred mirrors,they made a dummy profile of ship with 5 inch thick wood which ignited after focusing all the mirrors to a specific point on the ship. this experiment was then carried out again on a real boat in the water with the help of the 'mythbusters'.Thus proving Archimedes death ray as no longer a theory but a definitely possibility that this 'death ray' tactic was used against the roman ships in Syracuse.

Archimedes Death Ray: Testing with MythBusters

**Mathematics:**

Mostly known as inventor of mechanical devices, we cannot ignore Archimedes' contribution to Mathematics.

Being unhappy with the existing one, Archimedes is known to have invented his own Greek number system, so that he could accommodate more of his invented numbers.

According to some, the greatest invention of Archimedes is 'integral calculus'. Using this, he measured the section of areas surrounded by geometric figures. He broke the sections into a number of rectangles and then added the areas together. This principle is known as 'integration'. Also a part of the discovery of 'integral calculus' is 'differential calculus'. He calculated ways to approximate the slope of the tangent lines of his figures.

In the 'Measurement of Circle' Archimedes discovers the value of the square root of 3 as being more than 265/153 (approximately 1.732) and less than 1351/780 (approximately 1.7320512). The accurate value is rounded to 1.7320508076. He aquainted us with this principle without offering any explaination.

In 'The Quadrature of the Parabola', Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height.

In 'The Sand Reckoner', he set out the impossible task of calculating the number of sand grains the universe could contain. He challenged that it was not impossible to do, even if sand grains were too large to be counted. His friend King Gelo thought this was hardly possible. To solve the problem of sand grains, Archimedes invented a system based around the myriad or uncountable in Greek. It also denoted 10,000 in the Greek number system. He fixed a number system using powers of myriads (100 million) and finally calculated the number of sand grains in the universe as 8x1063 .

**Sites Referred:**

- http://en.wikipedia.org/wiki/Archimedes
- http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html
- http://web01.shu.edu/projects/reals/history/archimed.html