EUREKA - The Archimedes Principle

 

EUREKA    -     The   Archimedes   Principle

 

 

Since my primary education, I was startled by the word “Eureka” and origin of the word enthralled me.  It was related to Archimedes discovery known as “Archimedes Principle”.   In my childhood I used to shout “Eureka” whenever I found a solution to a problem or something new, out of sheer excitement.

Archimedes was born in 287 BC in the Greek colony of Syracuse a sea port in Sicily.  Archimedes was a genius in the fields of mathematics, physics and mechanical engineering. He was also an inventor, astronomer and weapon designer. He was the greatest scientist of the classical age.  He was a man who was of his time and far ahead of his time.  His father Phidias was an aristocrat and an astronomer.   Archimedes lived up to the age of 75 years.

Archimedes, the ancient Greek Scholar, when he stepped into the bath tub noticed that the  water level rose  - he  suddenly understood that the volume of water displaced must be equivalent to the volume his body part that  was submerged in the water and he shouted “Eureka!” in Greek that means I have  found it. 

“The buoyant force acting on a submerged or floating object is equal to the weight of the displaced fluid”

                                                           -         Archimedes principle. 

After this discovery he rose from the bath and ran without changing into clothes through the streets of Syracuse, Greece shouting Eureka.  He was overwhelmed with the realization of the invention that measurement of irregular object was possible.  He was so excited about the discovery and he ran shouting “Eureka!”  in his birthday suit  in the Syracuse streets to proclaim  it to the world.

The ancient scholars and scientists were found to be absent minded or eccentric and Archimedes was no exception.

Archimedes being the scientific advisor and related to  King Heiro II, once engaged a Goldsmith to make a crown and given him a bar of pure gold.  When the crown was made he found out that the Goldsmith cheated him using equal weight of Silver instead of pure gold.   This lead to Archimedes belief that not only the volume effect but also found an object’s density an important indicator of purity.  He found that the gold was more dense than silver.

Archimedes theory applies to buoyancy that things float in the fluid or water.  A copper ball in the water will sink whereas a wooden ball will stay afloat.  This great discovery of buoyancy led to the manufacturing of Ship or Vessel, so as the boat.

     “Give me a lever long enough and a fulcrum on which to place it       

And I shall move the world”.

                  -          Archimedes

Archimedes discovered levers, fulcrum and pulleys. 

The pulley reminds me of how we used to fetch water from a well in my native land by using a pulley, bucket and rope and later it was replaced by a motor engine.

There is an interesting story that his contemporaries challenged him to move a ship that endeavor would have deployed many hundreds of laborers to drag it.   They incited him saying that it will be proving his claim of -“give me a place to stand and I shall move the earth” - and you won’t believe that he did it so easily by using a compound complex pulley system.

This discovery led to modern era’s infrastructure built up cranes.  The Archimedes laws of lever resulted in first steam engine as well as Jet engine.

Archimedes’ discovery of spiral wheel resulted in the manufacturing of bicycle and gear byke.

I would like to mention here the famous quote of Felix Klien that –

    “The mathematicians like Archimedes,

    Newton and Gauss,

     Always united theory and applications in equal measure”.  

     

Archimedes found the number of diameters in the circumference of a circle.

Archimedes was an inventor.  He invented something called the Archimedes screw or Archimedean screw. The hydraulic screw has been used to lift water to higher levels for centuries. The Archimedean screw was originally used for irrigation in the river Nile. The Archimedean screw consists of a screw inside of a hollow pipe.  This screw is normally turned by a windmill or by manual labor. As the screw is turned at the tube, it scoops up volume of water.  The amount of water collected, slides up the spiral tube as crank is turned.  The water then spills out the top of the tube when it finally reaches the top.  In some of the developing countries Archimedes Screw is used for irrigation even in the contemporary world.

The Claw of Archimedes is a weapon that he devised in order to guard the city of Syracuse. The Claw of Archimedes is also referred to as “the Ship Shaker” comprised of a crane-like arm from which a large metal-grasping hook was hung. When the Claw was flung at an attacking ship, the arm would swing upward, lifting the ship from the water and perhaps even sinking it.  

Among the war machines attributed to him are Catapult – a mirror system for focusing the sun’s rays on the invaders’ ships and setting them on fire.

Integral Calculus - a mathematical theory that derives the areas and volume of spaces and the relationships between variables such as Speed, Distance and Time remains one of Archimedes greatest accomplishments.

Archimedes was one of the greatest mathematicians of all time.  He made a major contribution to the mathematical world and without Archimedes the mathematics would not have been the same. His writing was that of a genius. 

             “Mathematics reveal its secrets only to those who approach it

                with pure love, for its own beauty”

                                            

-           Archimedes

Another invention was that of a miniature planetarium, a sphere whose motion imitated the earth, sun, moon and the five planets that were then known to exist.

Archimedes lived in Syracuse except for his education in Alexandria, Egypt. Prior to Archimedes arrival in Alexandria, there lived a mathematician and great scholar named Euclid who influenced Archimedes’ works.  Alexandria in those days was famous for great learning and scholarship and was known as the intellectual capital of the world.

In the third century BC, Syracuse was a hub of art, science and commerce. Archimedes after his return from Alexandria spent rest of his life in Syracuse with his inventions and thought processes.  

Immersed in the scientific culture of ancient Greece, Archimedes blossomed into one of the finest minds that our world has known.

Archimedes established strong foundations in the field of Physics particularly in statics, hydrostatics, infinitesimal and explained the principle of the lever.

Archimedes achievements –

·         Archimedes principle of density

·         Siege machines

·         Screw Pump

·         Formulae for the volumes of surprises

·         Approximate value of “0”.

This brilliant personality’s inventions and theories benefited all forms of modern science. 

He made invaluable contributions to Geometry, Arithmetic and Mechanics.

Archimedes’ major works are -

·         The Sand Reckoner

·         The Cattle Problem

·         The Method of Mechanical Theorems

·         The Quadrature of the Parabola

·         On the Sphere and  Cylinder

·         Measurement of the circle

·         On Conoids and Sphereoids

·         On Floating Bodies

·         Stomachion

A sphere carved within a cylinder covers the tomb of Archimedes.  This is based on a remarkable invention made by Archimedes proving that the two thirds of the volume and the surface area of the cylinder (including the bases of the latter). This is considered as his greatest mathematical accomplishment.

Let me conclude with the couplet of Mikhail Lermontov –         

       “Oh vanity!  you are the lever by means of

        which Archimedes wished to lift the earth!”  

The contributions of Archimedes to the world was so vast that unmeasured laurels were showered upon the great mathematician and a genius from the time immemorial. There were many countries’ stamps, coins, monuments, institutions, scholarships and achievement awards named after him.