The Genius Of Syracuse: Archimedes’s Life And Legacy

Biography:

The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, and created inventions that served as a starting point for the further development of science. Legends about Archimedes were created during his lifetime. The scientist spent several years in Alexandria, where he met and became friends with many other great scientists of his time.

The biography of Archimedes is known from the works of Titus, Cicero, Polybius, Livy, Vitruvius and other authors who lived later than the scientist himself. It is difficult to assess the degree of reliability of this data. It is known that Archimedes was born in the Greek colony of Syracuse, located on the island of Sicily. His father, presumably, was the astronomer and mathematician Phidias. Plutarch also claimed that the scientist was a close relative of the kind and skillful ruler of Syracuse, Hieron II.

Archimedes probably spent his childhood in Syracuse, and at a young age went to Alexandria in Egypt to get an education. For several centuries, this city was the cultural and scientific center of the civilized Ancient World. The scientist presumably received his primary education from his father. After living in Alexandria for several years, Archimedes returned to Syracuse and lived there until the end of his life.

Engineering:

The scientist actively developed mechanical designs. He outlined a detailed theory of the lever and effectively used this theory in practice, although the invention itself was known before him. In particular, based on his knowledge in this area, he made a number of block and lever mechanisms in the port of Syracuse. These devices simplified the lifting and movement of heavy loads, allowing for the acceleration and optimization of port operations. And the “Archimedes screw”, designed for scooping water, is still used in Egypt.

Archimedes’ inventions: screw, spiral or “worm”

The theoretical research of the scientist in the field of mechanics is of great importance. Based on the proof of the law of the lever, he began to write the work “On the Equilibrium of Plane Figures”. The proof is based on the axiom that equal bodies on equal arms will necessarily be balanced. Archimedes followed the same principle of constructing a book – starting with the proof of his own law – when writing the work “On the Floating of Bodies”. This book begins with a description of the well-known law of Archimedes.

Mathematics and Physics:

Discoveries in the field of mathematics were a real passion for the scientist. According to Plutarch, Archimedes forgot about food and personal care when he was on the threshold of another invention in this area. The main direction of his mathematical research was the problems of mathematical analysis.

Even before Archimedes, formulas were invented for calculating the areas of a circle and polygons, the volumes of a pyramid, cone and prism. But the scientist’s experience allowed him to develop general methods for calculating volumes and areas. To this end, he improved the method of exhaustion invented by Eudoxus of Cnidus and brought the ability to apply it to a virtuoso level. Archimedes did not create the theory of integral calculus, but his works later became the basis for this theory. The mathematician also laid the foundations of differential calculus.

From a geometric point of view, he studied the possibilities of determining the tangent to a curved line, from a physical point of view – the speed of a body at any moment in time. The scientist studied a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to a hyperbola, parabola and ellipse. Only in the seventeenth century were scientists able to fully understand and reveal all of Archimedes’ ideas, which have survived to that time in his surviving works. The scientist often refused to describe his inventions in books, which is why not every formula he wrote has survived to this day.

The scientist considered the invention of formulas for calculating the surface area and volume of a sphere to be a worthy discovery. If in the previous cases described, Archimedes refined and improved other people’s theories, or created quick calculation methods as an alternative to existing formulas, then in the case of determining the volume and surface of a sphere, he was the first. Before him, no scientist had coped with this task. Therefore, the mathematician asked to carve a sphere inscribed in a cylinder on his tombstone.

Archimedes’ Law:

The scientist’s discovery in the field of physics was the statement known as Archimedes’ Law. He determined that any body immersed in a liquid is subject to pressure from a buoyant force. It is directed upward, and its magnitude is equal to the weight of the liquid that was displaced when the body was placed in the liquid, regardless of the density of this liquid.

There is a legend associated with this discovery. Once, Hiero II allegedly approached the scientist, who doubted that the weight of the crown made for him corresponded to the weight of the gold that was provided for its creation. Archimedes made two ingots of the same weight as the crown: silver and gold. Then he placed these ingots in a vessel with water one by one and noted how much the water level rose. Then the scientist placed the crown in the vessel and discovered that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus, it was discovered that the master kept some of the gold for himself.

There is a myth that a bath helped Archimedes make a key discovery in physics. While bathing, the scientist allegedly slightly raised his leg in the water, discovered that it weighed less in water, and experienced an epiphany. A similar situation did take place, however, with its help, the scientist discovered not Archimedes’ law, but the law of specific gravity of metals.

Astronomy:

Archimedes became the inventor of the first planetarium. When this device moves, one can observe:

• the rising of the Moon and the Sun;
• the movement of the five planets;
• the disappearance of the Moon and the Sun behind the horizon;
• phases and eclipses of the Moon.

The scientist also tried to create formulas for calculating distances to celestial bodies. Modern researchers suggest that Archimedes considered the Earth to be the center of the world. He believed that Venus, Mars, and Mercury revolved around the Sun, and that this entire system revolved around the Earth.

Personal life:

Much less is known about the scientist’s personal life than about his science. His contemporaries also composed numerous legends about the gifted mathematician, physicist, and engineer. The legend says that one day Hiero II decided to present a multi-deck ship as a gift to Ptolemy, the king of Egypt. It was decided to call the watercraft “Syracusia”, but it could not be launched.

In this situation, the ruler again turned to Archimedes. From several blocks, he constructed a system with the help of which the launch of the heavy vessel was made possible with one movement of the hand. According to legend, during this movement, Archimedes said:

"Give me a place to stand, and I will move the world."

Death:

In 212 BC, during the Second Punic War, Syracuse was besieged by the Romans. Archimedes actively used engineering knowledge to help his people win. Thus, he designed throwing machines with which the Syracusan warriors threw heavy stones at their opponents. When the Romans rushed to the city walls, hoping that they would not come under fire there, another invention of Archimedes – light throwing devices for close action – helped the Greeks throw cannonballs at them.

The scientist also helped his compatriots in naval battles. The cranes he developed grabbed enemy ships with iron hooks, lifted them slightly, and then abruptly threw them back. Because of this, the ships capsized and sank. For a long time, these cranes were considered something of a legend, but in 2005, a group of researchers proved the functionality of such devices by reconstructing them based on surviving descriptions.

Thanks to the efforts of Archimedes, the Romans’ hopes of storming the city failed. Then they decided to move on to a siege. In the fall of 212 BC, the colony was taken by the Romans as a result of treason. Archimedes was killed during this incident. According to one version, he was hacked to death by a Roman soldier whom the scientist attacked for stepping on his drawing.

Other researchers claim that Archimedes’ laboratory was the place of his death. The scientist was allegedly so carried away by his research that he refused to immediately follow the Roman soldier who was ordered to take Archimedes to the military commander. In anger, the latter pierced the old man with his sword.

There are other variations of this story, but they all agree that the ancient Roman politician and military commander Marcellus was extremely upset by the death of the scientist and, uniting with both the citizens of Syracuse and his own subjects, arranged a magnificent funeral for Archimedes. Cicero, who discovered the scientist’s destroyed grave 137 years after his death, saw a sphere inscribed in a cylinder on it.

Works:

1. Squaring the Parabola
2. On the Sphere and the Cylinder
3. On Spirals
4. On Conoids and Spheroids
5. On the Equilibrium of Plane Figures
6. Epistle to Eratosthenes on the Method
7. On Floating Bodies
8. Measurement of a Circle
9. Psammit
10. Stomachion
11. Archimedes’ Problem on Bulls
12. Treatise on the Construction of a Solid Figure with Fourteen Bases Around a Sphere
13. Book of Lemmas
14. Book on the Construction of a Circle Divided into Seven Equal Parts
15. Book on Touching Circles