# Archimedes

Archimedes has been described as one of the greatest scientists of the classical period. He made a number of advancements in the area of mathematics, geometry, engineering, and astronomy among others. He also designed a number of weapons that were used in the Second Punic War.

**Early Life**

Archimedes was born in Syracuse, Sicily in 287 B.C. There is very little known about Archimedes’s family although in one of Archimedes’s books (*The Sand Reckoner*), Archimedes mentions that his father was an astronomer. There is some evidence that Archimedes was related to the king of Syracuse, Hiero II but this has been called into question. Plutarch, a writer who wrote a book on the lives of famous Greeks (*Plutarch’s Lives*), states that Archimedes was related to the king. In fact, Plutarch states that the reason why Archimedes was so famous was because of being related to King Hiero II and being a close friend of King Hiero II’s son Gelon. Archimedes was a close friend of Gelon and Archimedesdedicated his book, *The Sand Reckoner*, to Gelon.

Archimedes spent most of his life in Syracuse although he did spend some time in Alexandria where he attended school. He studied at Euclid’s school in Alexandria with Euclid’s successors where he studied mathematics. After leaving Euclid’s school, Archimedes returned to Syracuse where he remained until his death in 212 B.C.

Archimedes was actually known more as an inventor than a mathematician until another mathematician, Eutocius of Ascalon, published a number of works by Archimedes. Most ancient writers focused on Archimedes’s invention and war machines.Archimedes was an excellent mathematician who would often become so focused on his work that he needed to be reminded to eat. He would often start drawing geometric figures on any surface he could find as well as in dust and ashes. One story claims that Archimedes began drawing geometric figures on his body while he was rubbing himself with olive oil after a bath.

Archimedes is considered to be one of the greatest mathematicians in the world by historians of mathematics. He was mentioned by a number of important classical mathematicians, such as Heron, Pappus, and Theon.

Only a few of Archimedes’s works survive. Most of them were lost after the library of Alexandria was burned down. Most of the work that still exists come from Latin or Arabic translations of the books.

**The Archimedes Palimpsest**

An amazing discovery that shed a lot of light on the work of Archimedes was made in 1906. Johan Heiberg, an Archimedes scholar, was in Constantinople, Turkey (now called Istanbul) and found a Byzantine prayer book that had been written in the thirteenth century. What makes the discovery important is that the prayer book had been written overtop of some mathematical texts. The person who wrote the religious texts had attempted to scrape away the mathematical writing before writing down the Christian prayers. As a result, only a faint trace of the mathematical work could be seen. The mathematical works that had been copied over were a number of works by Archimedes which had been originally copied in the book during the tenth century. This book became known as the Archimedes Palimpsest. A palimpsest is just an old document that has had the original writing erased and new writing added.

The Archimedes Palimpsest contained seven books written by Archimedes, including two that had never been seen before. One of these books, The Method of Mechanical Theorems, explained how Archimedes did mathematics. Archimedes wrote that this method may help future mathematicians find new theorems.

These new works showed how far ahead of his time Archimedes actually was. Some of his discoveries were not re-discovered for a long time.

**The Discoveries**

Archimedes made a number of astounding discoveries over the course of his life. Not only did he make a number of discoveries, he was able to use these discoveries to create machines and solve other problems.

**Archimedes’s Principle (The Law of Buoyancy)**

The story behind Archimedes discovering the law of buoyancy is probably one of the most famous stories about Archimedes. The story is passed down by the Roman author Vitruvius. In book 9 of his De Architectura, Vitruvius describes how the king of Syracuse had ordered a golden crown to be made. The king, King Hiero, gave the goldsmith the exact amount of gold that the goldsmith would need to make the crown. When the crown was finished, even though it weighed the correct amount, Hiero suspected that the goldsmith had switched the gold for some cheaper materials. The problem was that the crown had an irregular shape so even though people knew how heavy the crown was, they didn’t know the crown’s volume.

Hiero wanted to check to make sure that the crown was made completely out of gold, but he didn’t know how to do it without destroying the crown, which he didn’t want to do. He asked a number of expert, one of which was Archimedes, to figure out how to test the crown.

Archimedes discovered the answer one day while getting into a bathtub. Archimedes noticed that water was displaced from the tub as his body entered the water. He also noticed that he didn’t weigh as much when his body was in the water. According to the story, Archimedes screamed “Eureka” and ran down the street, naked and wet, to tell the king of his discovery.

With this discovery, Archimedes came up with the law of buoyancy (the Archimedes’s principle). The law of buoyancy states that an upward force (buoyancy) will be exerted on an object submersed in water that is equal to the weight of the displaced fluid. Another way of looking at this is that an object will lose weight when placed in a fluid that is equal to the amount of fluid displaced.

After making this discovery, Archimedes placed both gold and silver in cups of water and measured how much they displaced the water. He found that silver raised the water level higher than the same amount of gold (i.e., more water was displaced by silver). This is because silver has more volume than gold.

Archimedes knew how much gold the goldsmith had been given so he knew by how much that amount of gold should raise the water level. When he tested the crown, he found that the goldsmith had cheated and had created the crown out of cheaper materials.

**The Archimedes Screw**

The Archimedes Screw is a device that was developed to move water from a lower location to a higher location. It was originally developed to move bilge water out of a ship but was adapted to be used for irrigation. In fact, it is still being used today.

The Archimedes Screw is made up of a screw inside a hollow tube. As the screw is turned, the bottom part of the screw collects water and the water is pushed up along the screw as it turns.

**The Law of the Lever and Balance**

Archimedes did not invent the lever but he did figure out why they worked. Archimedes also discovered how easy it is to move large weights through the benefit of a block and tackle pulley system. In fact, according to Pappus, it was after discovering the advantages of levers and pulleys that he made one of his most famous claims to King Hieron. Archimedes stated that if he had a place to stand, he could move the Earth.

King Hieron challenged Archimedes to prove his claim. Using a series of pulleys, Archimedes picked up a fully loaded ship out of the water and then placed it on land all by himself. This task would have normally taken at least one hundred people.

While working on this law, he also developed one of the main concepts in physics—the center of gravity.

**Pi (π)**

Archimedes was also able to calculate a value for Pi that remained the most accurate calculation until the invention of electronic calculators in the late twentieth century. To calculate Pi, Archimedes did not take measurements, instead he worked the value out in his head by imagining various shapes placed inside and outside of a circle. He began by imagining two triangles—one inside a circle and one surrounding the outside of a circle. Both triangles touched the circle. Archimedes knew how to figure out the perimeter of the triangles so this gave him a range for the circumference of the circle. He knew the circumference was bigger than the inside triangle and smaller than the outside circle. Archimedes then used inside and outside hexagons to further refine his numbers. In the end, Archimedes came up with a number that was used for centuries and was 99.9% accurate.

**Other Discoveries**

Archimedes also came up with a proof to calculate the volume of a sphere. Archimedes was so pleased with this work that he requested the proof should be placed on his gravestone (which it was).

Archimedes also showed how big numbers could be written through the use of exponents and also showed that numbers written as exponents could be multiplied simply by adding the exponents together.

**The Second Punic War**

During the Second Punic War, the Romans attempted to conquer Syracuse. Archimedes was called upon to help with the defence of the city. To do this, Archimedes invented a number of machines that could be used to defend the city. Archimedes was so successful at stopping the Roman attack that the Roman commander Marcellus called off the attack and instead laid siege to the city.

**The Archimedes Claw**

While there is some debate over whether Archimedes Claws were ever built, a number of Roman historians mention huge wooden beams attached to the walls of Syracuse. These beams could be swung out as Roman ships approached. Some of the beams had weights on them that could be dropped, knocking holes into ships so that they sunk. Others had a hook on them that could catch the rigging or rails of a ship and either pick it up, shake it, or capsize it.

**The Death Ray**

Another device that it has been claimed Archimedes used was a “death ray”. This consisted of a number of bronze or copper shields that had been highly polished and placed on the wall so that the shields would catch the sunlight and concentrate the sunlight into one single, very strong beam of light that would set the approaching ships on fire.

This death ray is only mentioned by later writers and is not mentioned by any of the ancient historians. This has raised a lot of doubt about the claim. When students at MIT attempted to build Archimedes’s death ray, they were able to get some charring and flames on a test but it was not enough for a ship to burst into flames.

**Catapult and Stone Throwers**

Of all the weapons that Archimedes developed to hold of the Roman attacks, the catapults and stone throwers probably had the most impact. Archimedes built stone throwers that could shoot stones weighing more than 225 kilograms at enemy ships and soldiers. Polybius reports that the range of the stone throwers could be changed as needed.

Also, Archimedes used smaller and smaller catapults so that the Romans were constantly under attack as they approached. The smallest weapon was known as the scorpion. The scorpion was a small catapult or crossbow-type weapon that was attached to small windows or loopholes built into the city walls. They could be used by one person and could fire bolts or small iron balls at the approaching soldiers.

Archimedes’s machines helped to hold off the Roman siege and the city only fell when people within the city walls who supported the Romans opened the gates and let the Romans in.

**Death**

Archimedes did in 212 B.C. at the end of the Second Punic War. Marcellus, the Roman commander, had ordered Archimedes to be spared and brought to him because Marcellus was impressed with the way Archimedes defended the city, but he ended up being killed. Plutarch reported three different stories regarding how Archimedes met his death but they all agreed that he was killed by a Roman soldier when the Romans finally conquered the city.

The first story states that Archimedes was completely focused on a problem he was working on. He was so caught up in the problem that he never even noticed the Romans entering the city. When a Roman soldier commanded Archimedes to come with the soldier to see Marcellus, Archimedes refused until he had finished working out the problem. The Roman soldier became angry and killed Archimedes with a sword.

The second story is that a Roman soldier, with a drawn sword, came up to Archimedes and threatened to kill him. Archimedes asked the Roman soldier to wait until he was finished working on a problem. The Roman soldier responded by killing Archimedes.

The third story states that Archimedes was carrying various equipment with him on his way to see Marcellus. Some soldiers saw him and thought that he was carrying some gold so they killed him to get it.

Regardless of how he died, Archimedes was a true genius whose work inspired those who followed after him.