# Archimedes: biography and contributions to science of this Greek researcher.

**This was the life and scientific legacy of the Greek mathematician Archimedes of Syracuse.**

Classical Antiquity was a turbulent time but, at the same time, full of new advances and a development of science so significant that, if it had not been for the Middle Ages, we would surely have reached much further than we are now.

Despite the fact that the majority of the population was illiterate and uneducated, there were many great men who lived in that era, among them Archimedes, a great mathematician, physicist and inventor of devices for civil and, above all, military purposes.

Below we will see the life and great contributions to science of this researcher through this biography of Archimedes, and we will better understand how the bases, although primitive, of what with the passage of almost 2000 years would be our modern scientific method emerged.

## Archimedes of Syracuse: biography and contributions to science.

Archimedes was a mathematician, physicist, inventor, engineer and astronomer who lived in Ancient Greek times about 2000 years ago. At that time few people had the privilege of knowing how to read and write, so there are not many writings about him and all we know about this inventor is from oral tradition and testimonies of several classical writers, most of them later than Archimedes.

**His homeland was Syracuse, a city in Magna Graecia, a region located on the island of Sicily and the southern part of the Italian peninsula.**. The ruler of that city, who ruled it as a tyrant, was Hieron II, who is suspected to have been related in one way or another to Archimedes. Whatever their relationship was, both had a very interesting relationship, since Herion II trusted the mathematician to be an advisor and inventor for the defense of the city.

Little is known about Archimedes' family. Not much is known about his mother, but we do know about his father Phidias, an astronomer who transmitted his interest in the science of the firmament. It does not seem that he married or had children, and if he did, that was erased from the annals of history. Nor can we confirm whether he said his famous "eureka" while walking naked through the streets of his hometown, nor if he really said the phrase "give me a foothold and I will move the world".

### Early years

Archimedes was born in 287 BC in Syracuse, Sicily. Thanks to an excerpt from his book "The Sand Counter" we know that his father's name was Phidias and that he was a well-known astronomer of the time. Seeing that his son showed great abilities from an early age, Phidias decided to introduce him to the world of mathematics and astronomy.

Thanks to his great aptitudes and his good relationship with the king of Syracuse Hieron II Archimedes was sent to Alexandria in 243 BC, the center of science of the time, in order to expand his knowledge in mathematics under the teaching of the eminences of the time. Among his teachers was Canon of Samos, a great mathematician from whom the young Archimedes learned a great deal. After his stay in the Egyptian city, Archimedes returned to his homeland to begin his research.

### Service to the homeland

On his return from Alexandria Archimedes was accepted as advisor to Hieron II **was accepted as an advisor to Hieron II, in charge of designing systems and devices that would help the defense of the city.**. Under the protection and patronage of the monarch, the young mathematician had full freedom to do all kinds of experiments, as long as they benefited the king and Syracuse. With Hieron II as his patron, Archimedes would begin an era of extensive research and great advances.

One of the most important episodes of this period for his career was when the king ordered the construction of the largest ship ever made, with such bad luck that, when it was put to sea, it ran aground. Since even with brute force the ship could not be pulled out, Hieron II commissioned Archimedes to find a way to refloat it. So Archimedes devised a system of composite pulleys that increased the thrust force, moving the ship with little effort, laying the foundations of his law of the lever.

Another of the most important moments in Archimedes' life was when the king asked him to resolve a doubt that was keeping him awake at night. **The monarch wanted to know if his crown was really made of solid gold or if he had been deceived and its interior was made of a less valuable material....**. This problem proved to be a real headache for Archimedes, since he did not know how to solve this question without breaking the crown in two and looking inside.

The Greek scientist knew that he had to find the density of the crown, and since it weighed the same as a gold ingot, he had to find the answer in its volume. The problem was that there was no known way at that time to calculate the volume of irregular objects. Legend has it that he discovered how to do this while taking a bath. As he immersed himself in the bathtub, he saw the water level rise. The amount of water rising was directly proportional to the volume of the submerging body.

From this he concluded that, **if he submerged the crown and measured the variation in the water level, he could know precisely what its volume was.**. This was one of his great discoveries and, for this reason, was known as Archimedes' principle. It is said that, before such a discovery, he came out of the bathtub euphoric shouting "eureka", naked through the streets of Syracuse to the surprised gaze of passers-by.

### Conflict in Syracuse

During the year 213 B.C. **Roman soldiers attacked Syracuse and harassed its inhabitants into surrender.**. This action was led by Marcus Claudius Marcellus, a distinguished Roman soldier and politician baptized as the Sword of Rome, a key figure in the Second Punic War. The war lasted two years, in which the inhabitants of Syracuse fought against the Romans with courage, tenacity and fierceness, among them Archimedes who played a very important role in the defense of the city.

But unfortunately the city eventually fell. Marcus Claudius Marcellus, who knew the great intellectuality of Archimedes, explicitly ordered that he was not to be harmed or killed, since he wanted him among his advisors. However, **whether through the ignorance or ineptitude of his own subordinates, Archimedes died at the hands of one of the Roman soldiers in 212 BC.** in 212 BC. There are four versions of what happened.

### The four deaths of Archimedes

One version says that Archimedes was in the middle of solving a mathematical problem when the Roman soldier accosted him. The mathematician asked him**asked him for a little time to solve the problem and that must not have pleased the soldier, who decided to end his life.**and he decided to end his life.

Another version tells that Archimedes was solving a mathematical problem when Syracuse was taken. A Roman soldier entered his compound and ordered him to meet with Marcellus, to which the mathematician replied that he wanted to solve the problem he was working on. The soldier, annoyed by the reply, killed Archimedes in disobedience to Marcellus.

There is a third version that tells that Archimedes had in his hands a bunch of mathematical instruments. The soldier **soldier saw him, thinking that he must be carrying valuables or some kind of weapon to win over the Roman invaders.** to beat the Roman invaders, so without a second thought he took the mathematician's life.

Finally, the fourth and most realistic version tells that Archimedes was crouching on the ground, contemplating one of his plans. While he was studying it, he was approached from behind by a Roman soldier who, without thinking twice, killed the mathematician, **not knowing that he was dealing with the Greek genius, he decided to shoot him in the back.**.

### After his death

More than 130 years after his death, in the year 137 B.C., the Roman writer, politician and philosopher **Marcus Tullius Cicero held a position in the administration of Rome and wanted to find Archimedes' tomb.**. It was not easy, because Cicero could not find anyone to tell him the precise place where the mathematician had been buried.

Despite the unknowns and the total ignorance about where the remains of Archimedes were, Cicero managed to locate the tomb, very close to the gate of Agrigento. His resting place was in a deplorable condition, so Cicero decided to clean his tomb and, to his surprise, he found that **was inscribed on a sphere inside a cylinder, alluding to one of his discoveries.**.

## Contributions to science

Although the passage of time and the darkness of the Middle Ages meant that much of the knowledge of antiquity was lost forever, there is no shortage of knowledge attributed to Archimedes that has survived to the present day. Among the most outstanding are the following:

### 1. Archimedes' principle

**Archimedes' Principle is probably the most famous and important legacy of the Greek**. Quite by accident, Archimedes discovered the way to calculate the volume of any object, whether or not it had a regular shape.

This principle states that any body partially or totally immersed in a fluid (liquid or gas) receives an upward thrust equal to the weight of the fluid displaced by the object. In other words, depending on the volume of the object, the fluid will rise more or less, regardless of the weight of the object itself.

This principle not only made it possible to know the volume of any object, but also to know the volume of any object, **was instrumental in perfecting the buoyancy of ships, life preservers, submarines and hot air balloons, inventions that, although long after Archimedes, would not exist without his findings.**inventions that, although much later than Archimedes, would not exist without his findings.

### 2. Principle of the lever

Before modern cranes were invented, it was necessary to use brute force to move heavy objects. Constructing buildings was a labor-intensive task, and sometimes it was impossible to build them for lack of men.

Fortunately, Archimedes **found the solution by using one of the most basic and fundamental principles of physics and mechanics**. He observed that by placing an object on one end of a properly balanced board with a fulcrum, anything could be moved with relative effort.

### 3. Advances in mathematics

Many mathematical advances are attributed to the figure of Archimedes. Among them are precisely calculating the number Pi, making the first approximations to the system of infinitesimal calculus and discovering that the relationship between the volume of a sphere and the cylinder in which it is located is 2:3, something that was thus represented in his tomb in his honor.

### 4. Mechanical method

Another of Archimedes' most interesting contributions was the inclusion of a purely mechanical method. **the inclusion of a purely mechanical method in the reasoning and argumentation of geometrical problems, something unheard of in his time.**something unheard of in his time. Until that time geometry was considered a purely theoretical science and it was common to think that pure mathematics would descend to other more practical sciences that could be more useful for war and civilian purposes.

Archimedes, writing to his friend Eratosthenes, indicates that with his mechanical method he can address mathematical questions through mechanics. He also indicates that it is easier to construct the proof of a geometrical theorem if one has prior practical knowledge rather than hypothesizing theoretically. This new method of investigation would be the precursor of the informal **the precursor of the informal stage of discovery and formulation of hypotheses proper to the current scientific method.**.

### 5. The odometer

Surprising as it may seem, Archimedes invented the first odometer. Known as the odometer **it was a device built on the principle of a wheel that, when it turns, activates gears to calculate the distance traveled.** gears that make it possible to calculate the distance traveled.

### 6. The first planetarium

Based on the statements of many classical writers, among them Cicero, Ovid, Claudian, Marcianus Capella, Cassiodorus, Sextus Empiricus and Lactantius, Archimedes is considered to have invented the first planetarium.

**He probably built two, according to Cicero.**. One of them represented the Earth and several constellations near it, while the other, which had only one rotation, represented the Sun, the Moon, the planets that performed their own independent movements in relation to the fixed stars.

### 7. Archimedes' screw

Archimedes invented a screw that **allowed to transport water from the bottom to the top through a slope.**. According to Diodorus, this invention facilitated irrigation in the fertile lands of the Nile River in ancient Egypt, since traditional tools involved a lot of human effort.

This cylinder had in its interior a screw of the same length that kept interconnected a system of propellers that performed a rotary movement manually driven by a rotating lever. Thus, the propellers were able to push any substance from bottom to top, forming a kind of endless circuit.

### 8. Archimedes' claw

Archimedes' claw, also called the iron hand, **was one of the most fearsome weapons of war created by the mathematician, crucial in the defense of Sicily against the Roman invasions.** against the Roman invasions.

It was a large lever that had a grappling hook attached to the lever by means of a chain hanging from it. Through this lever the hook was manipulated in such a way as to rush upon the enemy ship, with the hook snagging it and causing it to either capsize or crash against the rocks of the shore.

Bibliographical references:

- Torres-Asis, A.K. (2010) Archimedes, the Center of Gravity, and the First Law of Mechanics: The Law of the Lever. Apeiron Montreal.
- Kires, M. (2007) Archimedes' principle in action. Physics Education.
- Parra, E. (2009) Arquímedes: su vida, obras y aportes a la matemática moderna. Revista digital Matemática, Educación e Internet.

(Updated at Mar 28 / 2023)