Archimedes’ principle

Background of Archimedes

Archimedes was born in 287 BC into a wealthy family of nobility and his hometown was a small village near to Greece. He also had a great father who was a great astronomer and mathematician. His father was very friendly to his children, thus Archimedes was greatly influenced by his father. This made him take a keen interest in mathematics, astronomy and ancient Greek geometry when he was a child. In 267 BC, Archimedes was 11 years old. At that time, his father sent him to Alexandria, Egypt and let him learn mathematics with Euclid’s student. Alexandria, located in the mouth of the Nile, was the knowledge and cultural center of the world at that time. There were also a lot of scholars and professionals in various fields. During his stay in this city, Archimedes met many mathematicians, and he learned a lot of knowledge and skills from them. This knowledge made a major impact for his scientific career and is also the basis of his science research in the future.

Achievements of Archimedes

Fig.1 Archimedes' principle

Fig.1 Archimedes’ principle. Image: Yupi666, via Wikimedia Commons.

Archimedes is considered by most great mathematicians as one of the greatest mathematicians of all time. And he had a lot of important achievements because of his early life of learning in Alexandria, Egypt. He was very good at learning, and this skill made him to find a way to solve areas, surface areas, volumes and other many geometrical objects. In addition to geometrical objects, he also had a important achievement in buoyant force. I think that Archimedes’ principle is his most important achievement. This principle told us the basic rule of buoyant force. According to Wikipedia, “the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.”[1] We also can express this principle by using a formula such that F = G (F is the buoyancy and G is the weight of the liquid that the object displaces ). Another different expression is  (ρ is the density of liquid, g is the acceleration of gravity, V is the volume of liquid).

Story of Archimedes’ principle

Fig.2 Archimedes run to palace

Fig.2 Archimedes runs to the palace. Image: Public domain, via Wikimedia Commons.

According to legend, one day, the king of Greece asked his craftsman to make a gold crown for him. However, the king suspected his crown was not made of real gold after his craftsman completed the crown. The king was afraid that his craftsman pocketed his gold. Although the weight of the crown is equal to the weight of gold that he give to the craftsman, but he could not destroy the crown and check. This question stumped the king and his chancellor. At that time, Archimedes had a very good relationship with the king of Greece and he was already very famous in Greece. After he listened to the suggestion of his minister, the king was going to invite Archimedes to test the crown. In the beginning, Archimedes also had no idea how to solve this problem. One day, he was about to bathe in his bath tub. When he got into the bath tub and saw the water spill, he suddenly had a good idea to solve the king’s problem. He thought that he could measure the displacement of a solid in the water and use this method to determine if the crown was made of real gold. And then, he excitedly jumped out from bath tub and ran to the king’s palace. He even forgot to wear clothes and he said “Eureka! Eureka!” (Eureka means “Found it!”) When he arrived at the palace, he immediately began to test the crown. He put the same weight of pure gold and crown into the two bowls that filled with full water and to compare the water of overflow. Then he found that the bowl with real crown overflowed more water than another bowl. It means that crown was made of other metals. This proves that the craftsmen deceived the king. The significance of the test is not that whether the goldsmith deceive the king, but Archimedes discovered the Archimedes’ principle.


Archimedes’ principle is a very important theory for the world. We can see that many modern inventions were made by using this theory, like big ships, submarine and so on. Thus Archimedes was really a great scientist, and he has made an indelible impact for social progress and human development.