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Math ISU

marina ch

on 21 January 2013

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Transcript of Archimedes

ARCHIMEDES •Archimedes was born in 287 BC in Syracuse, which was a Greek colony of Sicily at the time

•His father was Phidias who was a very famous astronomer.

•Archimedes was sent to Euclid’s school in Alexandria, Egypt, where he met many significant mathematicians and scientists.

•Going to Euclid’s school played a major role in his professional development Early Life Later Life After receiving his education he returned to Syracuse, which was at the time troubled with the Second Punic War.
Archimedes devoted his time to developing war machines in order to fend off the Roman army.
He invented devices such as; Archimedes' Claw, The Death Ray, catapults and many more War Inventions Archimedes' Claw Archimedes’ Claw was a device also used to keep the Roman ships away from the wall of Syracuse.
It was placed on the sea wall, and it was made of a hook which lowered once a ship approached.
The device would grab the ship, shake it vigorously and then toss it into the sea. This device was used in many battles and stopped many Roman ships. Archimedes' Death Ray Archimedes “Death Ray” was a device he invented to stop Roman ships from reaching the shore of Syracuse.
It was comprised of numerous large mirrors, suspected to have been polished shields,which reflected concentrated sunlight onto the attacking Roman ships causing them to catch fire.
The ray was used in only one battle as it was impractical Death of Archimedes Archimedes was killed by a Roman soldier, in 212 B.C.
He was unaware of his surroundings as he was busy making diagrams while trying to accomplish a new theory.
When he noticed the soldier he exclaimed " Do not disturb my circles!"
The ratio 2:3 and a figure of a sphere inscribed about a cylinder are engraved on his tombstone. Collaborations •Archimedes is not officially known to have collaborated with any mathematicians or physicists of the time

•He is however suspected to have been a student of Euclid, who contributed to his professional development.

•Archimedes also consulted Conon of Samos, Eratosthenes, and Dositheus about his projects before their publication. In Conclusion Archimedes was a significant mathematician, physicist, engineer, inventor, and astronomer, whose outstanding contributions in the field of science, mathematics and physics have brought about significant changes to the current world. Famous Quotes "Give me a place to stand, and I will move the earth." "Don’t disturb my circles." " Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." "Eureka, eureka!" "There are things which seem incredible to most men who have not studied Mathematics." "Soldier, stand away from my diagram." Mathematical Concepts •Throughout his lifetime Archimedes developed numerous concepts which were and currently are being further developed by numerous scientists and mathematicians.

•Those concepts include; the principle of buoyancy, the sphere cylinder ratio, the close approximation of pi and the method of exhaustion, the angle trisection theorem and many more The Principle of Buoyancy Archimedes principle states that any body completely or partially submerged in a fluid, at rest, is acted upon by an upward, or buoyant, force, whose magnitude is equal to the weight of the fluid displaced by the body Current Application of the
Principle Archimedes theory is applied in the manufacturing of submarines, ships, hot air balloons, and floating instrument platforms (also referred to as FLIPs).
FLIPs are research vessels which study waves in deep waters. They are originally put into the water in a floating horizontal position. They operate by pumping water into their stern tanks, which brings them to vertical positioning. The Story Behind Archimedes'
Discovery of Buoyancy Archimedes was commissioned by King Hiero II of Syracuse to determine if a golden crown made for him was made of pure gold. The problem was determining the concentration of the crown without damaging it. Archimedes was puzzled for a while. One day as he visited the public baths he noticed the displacement of the water as he entered the tub. At that moment, he discovered the theorem of buoyancy. He was so thrilled with his discovery that he immediately jumped out of the bath and ran naked onto the streets shouting “Eureka” (meaning I found it). The Approximation of Pi •Archimedes is credited with the first close approximation of pi.

•He suggested the ratio while working with the Eudoxean Method, also known as the “Method of Exhaustion

•Archimedes suggested the ratio after considering the perimeters of regular polygons which he circumscribed about the circle. He kept doubling the figures until he established 96sided polygons. Current Use of the Theory Archimedes’ close approximation of pi has directed numerous mathematicians to discover geometric formulas which are used today to solve innumerable problems. In addition, Archimedes’ discovery of pi was revolutionary as it further introduced the Eudoxean Method, a method which may be used to solve numerous problems. The Sphere/Cylinder Ratio •Archimedes discovered the surface area and volume of a sphere by comparing it to those of a cylinder.

•He suggested that the surface area of a sphere is four time that of its greatest circle, therefore he discovered the formula for the surface are of a sphere, which is SA = 4pr^2

•He then discovered the volume of a sphere by inscribing it in a cylinder and suggesting that it is two thirds of its volume, therefore the volume of the sphere is V = 4/3pr^3

•These formulas are used today in solving geometric problems and developing devices such as canons etc. Archimedes' Screw •It is a device used to rise from one level to another. Its consists of a circular pipe and a spiral, also known as a helix, which are inclined, while the lower part of the device is placed in water.
•The device is in rotation by a handle, attached to the helix, which causes the water or any other substance to move from one level to another. Current Uses Of Archimedes' Screw •The device was originally designed to remove water from the hold of a ships.

•Currently it may be used in developing countries fro the transportation of water and occasionally grains

•It is also used in waste water treatment plants for pumping sewage in treatment plants, as the design of the screws prevent clogging the volume of displaced fluid is equivalent to the volume of an object fully or partially immersed in a fluid the weight of the displaced portion of the fluid is also equivalent to the magnitude of the buoyant force an object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced The Three Major Points of the Principle " Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." Significance of Quote
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