Hello everyone! This video is about Archimedes, the ancient Greek mathematician who claimed he could move the Earth if he would have been given a stand. He stated : “Give me a place to stand and I will move the Earth.” Archimedes.
He was born in 287 BC in Syracuse, Sicily which at that time was a Greek colony. His parents named him Archimedes which means master of knowledge. When he found out the meaning of his name, he became determined to earn his name.
His father was an astronomer and he transmitted Archimedes his passion for mathematics stars and planets. He was asking his father lots of questions about star positions and cosmos. Because he loved to study, he was sent to Alexandria, and he became a scholar at the Library of Alexandria and the Moseion. He studied mathematics under Euclid students. When he came back to Syracuse, he tried to use mathematics to ease humans’ life.
He was concerned about irrigation, and he used his mathematics knowledge to create Archimedes screw. This was a device used to carry water up from a river and to irrigate fields and is still used today in many situations. Archimedes laid the foundation for building other aquatic screws : the steam propellers and plane propellers are other applications of Archimedes screw.
Archimedes became a famous scholar, and he was protected by Hiero, the king of Syracuse.
The way Archimedes discovered the dis-placement of liquids is well known and is interesting. King Hiero II , or Heron of Syracuse, ordered a crown of gold for himself to be made, and when it had been completed and delivered, he had his doubts about the honesty of the goldsmith, and called to Archimedes to tell him whether the crown was of gold, pure and simple. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body to calculate its density.
Archimedes was puzzled and went home deep in thought. Still considering the problem he went to the bath, and his bathroom was filled it to the brim while he was thinking of a solution for this math problem. Stepping in the bathtub he spilt a considerable quantity of water, and at once the idea struck him that any object or body put into water would displace its own bulk of the liquid.
He did not wait to dress, but ran half-naked to the palace, crying out, Eureka, Eureka! Meaning in Greek : I have found it; I have found it! What had he found ? He had solved the problem. He got a lump of gold the same weight as the crown and immersed it in water. He found it and weighed it as the crown. Both objects displaced different amounts of water demonstrating that Hiero’s crown was made of a different metal (silver most likely) than pure gold which had less density and was cheaper.
Archimedes thus discovered something simple and amazing: Any object would remove an amount of water directly related to its weight and volume when floating or immersing into water. He discovered that higher density objects at the same volume remove more water than lower density objects. He established thus the relative density and was the first to understand that gold for instance has a different density than silver or lead.
This is called the Law of Archimedes and it is used in many settings. The law of Archimedes explains why a boat floats and why it sinks if filled too much or filled with water like Titanic sank after hitting an iceberg.
He established Archimedes’ Principle which states that a body immersed in a fluid experience an upthrust equal to the weight of the fluid displaced, and this is fundamental to the equilibrium of a body floating in still water.
In On Floating Bodies, Archimedes suggested that (c. 246 BC):
Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object. A body immersed in water, or any fluid is pushed up with a force equal with the weight of the fluid dislodged.
Archimedes also discovered that the surface of any fluid in resting state is curved just like the Earth surface and the center of this circle is the center of the Earth. Thus, he demonstrated again what Eratosthenes of Cyrene did : the Earth was round.
Archimedes laid the foundations of hydrostatic science. Only 1800 years after Archimedes, Blaise Pascal would bring new contributions in the field of hydrostatic science.
Archimedes also established and demonstrated the lever law. The longer the lever is, the less force needs to be used to raise a heavy object.
“Give me a place to stand and I will move the Earth.”
His protector Hiero asked him to raise a boat. At his request Archimedes stated : “Give me a place to stand and I will move the Earth.” He successfully moved the boat that Hiero had built. His principle of lever is used today in many situations and makes our life easier. Grace of his levers many heavy objects were moved easily and thus architecture and constructions improved. He laid the foundation to build pulleys, cranes, and winches.
He discovered and understood the laws of levers. A lever could be a stick or a rod. A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. He created pulleys.
A pulley is a first-class lever and so is a screwdriver or a hammer. An oar and a wheelbarrow are second class levers, and a rod, a baseball bat and a shovel are third-class levers. A pulley is a lever too and so is an axle wheel used for instance for a windlass. A windlass has many uses such as a well, a capstan or a crossbow. Archimedes created himself many of these machines or laid the foundation to invent them. He was so confident in his machines and mathematical calculations that he stated : “Give me a place to stand and I will move the Earth.”
A lever to move Earth would be 1,41 X 10 to power 23 km or 88.X 10 to power 21 miles.
Syracuse was involved in the First Punic War and king Hiero asked Archimedes to use his mathematics knowledge in warfare to defend Syracuse against Roman Empire. When he was 70 years old Archimedes created a modern catapult and a crane with a hook to catch and raise Roman ships during the siege of Syracuse known as the Claw of Archimedes.
When Syracuse was finally conquered by the Romans a roman soldier entered Archimedes yard. He was making geometry drawings on the sand while solving a math problem. Many times, he was absorbed in drawing geometry figures on the sand in front of his house. The soldier asked the busy scientist to follow him, and Archimedes replied he was busy with a math problem and poked the soldier with his wooden stick. The Roman soldier stabbed Archimedes due to this argument and thus the scientist passed away.
Archimedes may have used mirrors acting collectively as a parabolic reflector to burn ships attacking Syracuse during the siege of Syracuse (c. 214–212 BC) and thus Archimedes destroyed enemy ships with fire. The device, sometimes called the “Archimedes heat ray”, was used to focus sunlight onto approaching ships, causing them to catch fire. In the modern era, similar devices have been constructed and may be referred to as a heliostat or solar furnace.
This purported weapon has been the subject of an ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship.
In the field of astronomy Archimedes agreed with Aristarch who believed the Earth was turning around the Sun, but he believed the Universe was a sphere and the Earth orbit was a circle on a sphere with the Sun in the center and the stars where fixed on a larger sphere. He asked himself questions about how large the Universe was and he probably felt it was infinite because he had interest in calculating very large and infinite numbers.
He tried to calculate the Earth and the Sun sizes, and he understood they were much larger than his predecessors and contemporaries thought. He disagreed though with his friend Eratosthenes of Cyrene who calculated the Earth radius correctly. Archimedes has built an astronomical device with concentrical spheres in order to create a calendar which was quite precise. It was a sphere, and the planets of the Solar System were turning around the Sun. This device is described in the work On Conoids and Spheroids.
Archimedes has foreseen the concept of gravity but not at the level of Isaac Newton. He was calculating in his studies for the lever laws the center of weight of many objects.
In mathematics Archimedes brought significant contributions.
He was the first to calculate the surface and the perimeter of a circle. He found a way to approximate the surface of a circle with the surface of a surrounding square then polygon. He thus discovered the number of Archimedes or pi number. His method to approximate the pi number is actually the act of birth for calculus.
He discovered that the ratio between the volume of a cylinder and a sphere inscribed is always 3/2. He felt that this observation was so important, and he was so excited to have understood that, that he wanted this drawing to be placed on his stone grave which did happen.
He brought significant contribution to the algebra : Ancient Greek numbers were difficult to use. He was curious about very large numbers or even the concept of infinite. He created a famous math problem the
Archimedes’ cattle problem which was solved correctly only in the middle ages. This was an example of the use of very large numbers and its result is indeterminate. Again , having interest in very large numbers and the concept of infinite he tried to count the sand particles in the universe in his work The Sand Reckoner.
There is an Archimedean Oath similar to Hyppocratic Oath and is used for engineers in more and more Universities.
Works by Archimedes :
Archimedes’s cattle problem, Book of Lemmas, Measurement of a Circle, The Method of Mechanical Theorems, On Floating Bodies, On Spirals, On the Equilibrium of Planes, On Conoids and Spheroids, On the Sphere and Cylinder, Ostomachion, Archimedes Palimpsest, Quadrature of the Parabola, The Sand Reckoner
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