Chapters

While mathematics often comes under criticism by students for its inability to be applied in daily life, the discipline was actually founded by trying to **make life simpler**. Division, multiplication, addition, subtraction – maths should help students obtain a better quality of life. One example of this can be found by reviewing the history of mathematics and examining the life of Archimedes of Syracuse. A great scientist, physician, mathematician, and engineer of ancient Greece - Archimedes utilized maths in order to explain the mechanics of daily life. He **contributed a number** of revolutionary tools, like the lever and the screw, through his mathematical works and explorations. Alongside the likes Newton, Pythagoras, Thales, Descartes, Einstein and others - Archimedes finds a place amongst the some of the great mathematicians and scientists in the history of the mathematical world. Keep reading to discover how!

## Who is Archimedes of Syracuse?

Like many scientists of antiquity, the life of Archimedes of Syracuse was not well documented. There is **no biography** that was written by him and, in fact, only a couple of written texts have been found about the mathematician - a common problem for historians studying this era. What we do know comes mainly **from the writings** of Isadore of Miletus, who discussed him in approximately 530 BCE. Some other scholars that mentioned the life of Archimedes range from Polybius (202-126 BCE), Plutarch (46-125BCE) and Livy (59-17BCE). It is estimated that Archimedes was born in Syracuse in 287 BCE. With an astronomer for a father, Archimedes began to take an interest in and study sciences from a young age. According to texts documenting some exchanges that Archimedes had with certain professors, historians were able to glean that **he continued his studies** at the reputable School of Alexandria.

It was there that he rubbed shoulders with the most well known sages of the era, most notably Dositheus, Conon of Samos and also the director of the library of Alexandria, Eratosthenes. **It was to this audience** of distinguished academics, and to the academics later inspired by these works, that Archimedes intended his scientific books. Later in life, Archimedes became an engineer for the king of Syracuse, Hiero II. He participated, therefore, in the **defense of the city** during the second Punic War. Legend has it that Archimedes was killed in 212 BCE by a roman soldier who had specifically been ordered not to execute him. The documents that have been gathered on Archimedes’ life are not enough to establish whether or not the scientist had any wife or children. On the other hand, documents found only concern the work and publications of the mathematician. **Nothing else has been found** over the period he was an engineer of the king. It is necessary then to trust the witness accounts found many years after his death. Archimedes and his seminal works made an important mark not only on his era and but also the generations to come. In other words, it was not only the great sages of his epoque that admired him, but he also** inspired** many other academics in the future. These great academics include Cicero, Plutarch and even Leonardo de Vinci. Archimedes’ influence even extends to language. The word “Eureka” was made popular by Archimedes, who it is said cried it out in the street to celebrate on of his major discoveries. The word eureka translates into “I have found,” which **explains why so many of us** have uttered it after having found an object or idea we thought we had lost. This alone is proof that Archimedes’ influence has traversed the ages. For more mathematicians from antiquity, check out the infamous Pythagoras!

## Archimedes Facts and Discoveries

Archimedes contributed to advancements in mathematics and the history of sciences. Here we give an outline on some of his **greatest** discoveries. **The Method of Exhaustion** Archimedes built upon the works of Eudoxus of Cnidus, which discussed how the method of exhaustion can be utilized in order to succeed in calculating the area found under a parabola. This permitted him to **continue to expand** upon his reflections on conic shapes, as well as calculate areas that were considered impossible to calculate before. **The Number Pi** Archimedes is particularly known to have calculated pi to **incredible precision**. To perform his calculations, the mathematician utilized regular polygons and combined this to calculate the relationship between the perimeter of a circle and its diameter. It was using this method that he was able to find the number that approached the number pi as we know today (3.14159).

Check for Maths tutor in Southampton here on Superprof.

**The Spiral of Archimedes** The mathematician studied the composition of the spiral. After many calculations, he **therein deduced** that the area of the spiral was equivalent to the radius of the circle that continued it. He also used the tangent to establish an equation of the circle (one segment where the length is equal to the circumference of the given circle). **The Formulas for Volume** The scientist made it a priority to calculate the areas and volumes of different objects. He utilized most notably his knowledge of mechanics in order to apply them to math. Archimedes wrote the treaty “Of the Sphere and the Cylinder” in order to **demonstrate the relationship** between the volumes of a ball and a cylinder. That is, if the ball was tangent to the cylinder by the lateral face and its two bases, the volume was equal to 2/3. This also gives the relationship between their surfaces. The study of areas and volumes of the sphere and the cylinder **were so important** to him that he even asked that the figures be inscribed onto his gravestone! Arithmetic, geometry, reasoning, mathematics, equations, prime numbers, algebra, differential calculus, integral calculus, decimals, pi, right triangle, complex numbers – all of the history of math was **marked by the advances** made by Archimedes. Mathematics courses at the starting level of high school can thank the celebrated Archimedes – as he has formed the basis of much of the maths or physics curriculum. Interested in learning more about the origin of other great ideas? Make sure to check out other famous mathematicians throughout history, like Thales and Sir Isaac Newton!

## Archimedes and the Flotation Principle

One of Archimedes’ most celebrated discoveries can be found in his “treaty of floating bodies,” which explains a vital part of the movement and laws of fluids through what is now known as the “principle of flotation.” Explaining this principle, Archimedes noted the **behaviour of solids** submerged in fluid. According to Virtruve, Archimedes studied the behaviour of water by taking a bath himself. The flotation principle is then the principle that describes the force subjected onto a solid body by gravity when it is submerged in either a liquid or gas. This force is explained by Archimedes by the **augmentation of the pressure** of liquid in the object. This pressure is physically more strong on the base of the submerged body than on the top, which causes the body to float because of this uneven force. Archimedes’ principle is **defined** as:

“Any body that is submerged, either completely or partially, in a fluid at rest is subjected to an upward force. The magnitude of this buoyant force is equal to the weight of the fluid that the body has displaced.”

Some important distinctions are made by Archimedes’ principle, namely that this push only operates on the object if the fluid and the body area at rest. This principle is **proved in his work** through his experimentation with cylindrical objects. While this principle continues to have an important impact in today's technological advancements, it was especially important at the time. Archimedes utilized this principle to **create the plans** for the biggest boat of antiquity for Hiero II: the Syracusia. Today, this principle is still being utilized in the construction of machines. Discover the best maths tutors in the UK here.

## Archimedes' Advancements in Mechanics

Similar to today, the discipline of mathematics during ancient times was entirely linked to discovering the functioning of the world. The **people who make up** the canon of the great academics of antiquity all studied and utilized math to put their world into context. Astronomy, geography, physics, mechanics - all scientific subjects need math.

Archimedes took a special interest in studying the function of machines and, in fact, is **widely recognized** as the father of static mechanics. At first, he studied the functioning of both the lever and centers gravity, **investigations** which would later play a major role his work “On the Equilibrium of Planes.” It was because of this work that Archimedes declares famously: “Give me a place to stand on and I will move the earth.” Archimedes wrote many other works relating to the principles of the mechanisms of the lever. Through these, he **discovered that weight** should be in equilibrium of each side of an object in order for the center of gravity to be in complete balance. The mathematician is also credited as providing the first investigations on machines using traction. One example is his implementation of the system of the pulley, which helped the ancient Greeks lift heavier objects. However, it is another, **more powerful invention** that is credited to the accomplished mathematician: the screw. Inspired by his discoveries in Egypt, Archimedes created the screw in order to help people lift water from rivers. Another one of Archimedes’ inventions, the “Antikythera mechanism,” permitted humans to be able to predict the dates and hours of eclipses. Some parts of this machine** are visible at** the National Archaeological Museum in Athens. For Archimedes, all of his mechanical inventions and academic investigations were not just distractions or entertainment. His discoveries were mostly a product of the commands to **protect the city** of Syracuse, and his creative spirit.

Find other math teacher here on Superprof.

The platform that connects tutors and students