Archimedes of Syracuse

Greek mathematician, scientist and inventor Archimedes regarded as one of the leading scientists and inventor of all time though there are very much a few details of his life mentioned. He made a lot of greatest contribution in science, mathematics, astronomy, mechanics and engineering for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder.

He is known for his formulation of hydrostatic principle commonly known as "Archimedes Principle" and at the same time he is the first who recognize and used the power of lever. Surely, he is one of the gifted mathematician that ever exists in his era.

A Closer Look.

Archimedes of Syracuse was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children. During his youth Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred to Conon of Samos as his friend, while two of his works (The Sand Reckoner and the Cattle Problem) have introductions addressed to Eratosthenes.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

Archimedes died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.

The last words attributed to Archimedes are "Do not disturb my circles", a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is often given in Latin as "Noli turbare circulos meos", but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch.

The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter. Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily. He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location. Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.

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Reader's Review:

The thought of a man running naked through the streets shouting with joy over a physical and mathematical discovery is one to warm the hearts of all who value knowledge. When Archimedes experienced this flash of joy, little did he know that his actions would become the genesis of a legend that would last for thousands of years. However, he should be remembered for so much more than that and several of his significant mathematical contributions are explored in this book.

It is really amazing to realize how close he was to inventing calculus 22 centuries ago, which was 18 before Newton and Leibniz. With notation that was minimally expressive, he was able to solve problems using a technique that demonstrates at least a rudimentary understanding of the concept of a limit. While many different problems can be solved using calculus, it only takes one breakthrough solution to demonstrate how it can be applied to so many of the others. It can be plausibly argued that algebraic and decimal notations would have been the tools that would have allowed him to overcome those last barriers. One can only speculate on how that would have changed history.

The book is not exhaustive and no attempt is made to make it that. Ten of his most significant discoveries are presented and the solutions are those of Archimedes, although modern notation is used. While the proofs are generally easy to follow, one is often left in awe as to how he thought of how to approach some of these solutions. The explanations are succinct, yet thorough, which is the signature of a solid storyteller.

Given the answers to the question posed in the title of this book, one can pose another that logically follows. Was Archimedes the greatest mind of all time? If the legends are correct, then the answer is probably yes. However, even if the unconfirmed stories are false, the mathematical and mechanical discoveries should make him a legend for more than one short stint of becoming a 'natural man.' -Charles Ashbacher

• His invention of the water-screw, still in use in Egypt, for irrigation, draining marshy land and pumping out water from the bilges of ships.

• His invention of various devices 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". (This saying of Archimedes is even more grandly laconic in Greek, in which it transliterates as the eight word sentence "dos moi pou st kai kin t&eacuten g&eacuten". See the reference to T L Heath at the end of the following section.)

• His discovery of the hydrostatic principle that a body immersed in a fluid is subject to an upthrust equal to the weight of fluid displaced by the body. This discovery is said to have inspired his famous cry "Eureka" ("I have found it").

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. This is a most beautiful piece of mathematics.

He computed the area of an ellipse by essentially "squashing" a circle.

He found the volume and surface area of a sphere. Archimedes gave instructions that his tombstone should have displayed on it a diagram consisting of a sphere with a circumscribing cylinder. C H Edwards (see reference below) writes how Cicero, while serving as quaestor 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."

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 seventeenth century AD. He found the volumes of various "solids of revolution" obtained by rotating a curve about a fixed straight line.

Source

Archimedes of Syracuse by Naiza Oclares is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
Based on a work at www.squidoo.com.