"Inventors and innovators: our heritage and our future"
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Archimedes
Table Of Contents
Today we will examine Archimedes’ life and work in various aspects such as: 1. Physics 2. Engineering 3. Astronomy 4. Mathematics Pic 1. Archimedes Thoughtful, by Domenico Fetti in 1620 AD
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Biography Let’s take a glimpse into the famous scientist’s life
Archimedes
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Archimedes of Syracuse (c 287 - c 212 B.C.) was a Greek mathematician, physicist, engineer, inventor and astronomer. Although little is known about his life and a significant part of his work was destroyed through the aeons, he is widely accepted as on of the greatest scientists of the classical antiquity.
What is known about his life:
He lived at: â–Ş Syracuse (a Greek Colony in Sicily, Southern Italy where he spent most of his life) â–Ş Alexandria (Northern Egypt, where he studied at the Great Library and met other leading minds of his era such as Conon of Samos and 6
Pic 2. Cicero visiting the tomb of Archimedes by Benjamin West
His death:
He was killed by a Roman soldier once the Syracuse Siege ended, during the Second Punic War. It is strange however, that the Roman commander had ordered his troops not to touch Archimedes. 7
Pic 3. The death of Archimeds by Thomas Degeorge (1815)
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Astronomy
Early years:
Pic 4. Archimedes shown to lift the world up using a lever 9
It is said that Archimedes due to his father, Phidias,who was an astronomer, had his first experience with astronomy in a surprisingly young age. He liked watching his father work, trying to calculate Earth’s volume and its distance from the Sun.
His theory
Archimedes strongly believed that the universe was tremendously bigger than what the others believed at that time, and that the Earth orbits around the Sun! Both of these two points were right.
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However, he made an important mistake.
He supported that the Earth was also much bigger, and calculated it’s perimeter to be 3 million stadia.
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Eratosthenis conducted his famous experiment in Alexandria. Using some of his astronomical observations and simple geometry he found out accurately that the actual value of Earth’s perimeter was 300.000 stadia.
He may had been wrong but it is really interesting that two extraordinary minds of that era challenged each other like that.
His work:
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Of course, what we mentioned above is not enough to characterize Archimedes an astronomer. He did much more than that. â–Ş He created a machine to calculate the duration of a year. After his death in 212 B.C it was moved to Rome, where it was studied by many scientists.
Pic 5. Modern portrait of Archimedes
His work:
Furthermore he created an astronomical machine that involved glass spheres which were moving with water, showing the position of the 5 planets that were known back then. It is said that he had calculated the distances between them accurately. In fact, it is considered to have been the first planetary system model. Finally, he made an astonishingly accurate hydraulic watch, that helped him calculated the celestial movements much easier. 13
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Mathematic s
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Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola. He also made an astonishingly Picaccurate 6. Portrait of Archimedes with the phrase “Αρχιμήδης ο calculation of π. Γεωμέτρης” written on its hat, emphasizing on his achievements in the field of Geometry
Plutarch in Parallel Lives said: “
He(Archimedes) placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.
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His work on circles:
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Pic 7. His work on circles is considered so great that this specific type of circle has been named after him (Archimedean Circle).
In his book, Κύκλου Μέτρησις, he calculated that the actual value of π was between 31⁄7 (which is almost 3.1429) and 310⁄71 (almost 3.1408). He was right, because the real value, 3.1416, is within these boundaries. Moreover, he proved that the area of the circle is the result of π
Archimedean Property:
There are two numbers, x and y. The only constraint here is x > 0. According to the Archimedean property, for any number x there is a number n that verifies the thesis following: 18
nx > y
“If a number is added to itself enough times it will become greater than any other.�
Parabola:
In “The Quadrature of the Parabola� , Archimedes proved that the area covered by a Parabola and a straight line is equal to the 4/3 of the area of an inscribed triangle, using the method of exhaustion and eventually reaching an infinite geometric progression with ratio 1/4
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3.14159265358... Archimedes’ calculation on π has been of great use for many scientists through the aeons. 20
Spheres and cylinders:
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In his book, “On the Sphere and Cylinder”, Archimedes has reached to some quite interesting conclusions. The most important among them was that the area and volume of a sphere is equal to the ⅔ of the circumscribed cylinder. Pic 8. Image showing a sphere inside a circumscribed cylinder
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Physics
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Eureka!
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Reportedly exclaimed by Archimedes upon discovery that the volume of displaced fluid is equal to the volume of the submerged object. Archimedes also used this principle to help Hiero II with his problem with a golden crown.
An explanation worth writing:
You may wonder why was our previous slide designed like that. Well, “Eureka” undoubtedly holds a position among the most well-known phrases worldwide and is indirectly connected to Archimedes’ most important achievement in Physics. It is related to the Archimedes’ Principle. Pic 9. Archimedes saying Eureka. (Historically inaccurate but is still 24
a quite good and funny depiction of the event.)
The Story behind this principle:
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According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be Pic 10. Archimedes’ experiment used to determine the volume.
Archimedes Principle:
“Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object�
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Applications of his principle in everyday life can be seen in : 1. Shipbuilding 2. Submarines , that need to constantly change their flotation values in order to reach greater depths or to return to the surface
Law of the lever:
Archimedes also spent time working with levers, which contributed in his legendary achievement of pulling a ship by using only his left hand. He summed up his knowledge in the following phrase:
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If the distance a from the fulcrum to where the input force is applied (point A) is greater than the distance b from fulcrum to where the output force is applied (point B), then the lever amplifies the input force. On the other hand, if the distance a from the fulcrum to the input force is less than the distance b from the fulcrum to the output force, then the lever reduces the input force.
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Engineering
A picture is worth a thousand words
Pic 11. The Siege of Syracuse 29
Archimedes also made a lot of contributions in engineering. During the Siege of Syracuse(213212 BC), he invented a lot of defense systems in order to protect his city.
The “Iron hand”
This distant ancestor of the modern crane was used against enemy ships, that tried to conquer Syracuse.
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Pic 12. The “Iron hand” in action
The “Iron hand” lifted the enemy ships with a hook and then, the operators cut the rope holding the chain of the hook so that the hovering ship would be crushed against the water or adjacent rocks.
Steam Cannon
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Pic 13. The cross section of the Steam Cannon
It was a cannon which functioned with steam. It consisted of a metal cylindrical boiler which was connected to a closed reservoir of water with a valve. When the boiler acquired the appropriate temperature with the fire, the valve was opened, the water poured into the boiler, it evaporated rapidly and the projectile was launched.
Archimedes’ screw
Pic 14. Archimedes’ screw 32
Archimedes' screw is a mechanism for pumping water with a small difference in height. It consists of a screw (a helical surface surrounding a central cylindrical shaft) inside a hollow pipe.With the manual rotation of the screw, the water (trapped within its coils) rose and flowed from the mouth of the pipe.
Uses of Archimedes’ inventions in our daily life
Pic 16. A modern crane designed like the “Iron hand”, but for different purpose
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Pic 15. Archimedes’ screw used to drain poldgers from a lake in Netherlands
Bibliography
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Archimedes Astronomer
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https://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B9%CE%BC%CE%AE%CE%B4%CE% B7%CF%82
2. 3. 4. 5. 6. 7. 8. 9. 10.
http://www.academy.edu.gr/Antikythera-Digital-Book-Files/VI_ALL_185_200.pdf https://www.britannica.com/biography/Archimedes http://www.newworldencyclopedia.org/entry/Archimedes https://www.arcmeletitiki.gr/images/uploads/pdf/arc_arx5.pdf http://www.mathlab.upatras.gr/wp-content/uploads/2013/09/Αρχιμήδης.pdf http://thesis.ekt.gr/thesisBookReader/id/3469#page/134/mode/1up http://news.in.gr/science-technology/article/?aid=1500028657 https://en.wikipedia.org/wiki/Archimedes http://www.mathlab.upatras.gr/wp-content/uploads/2013/09/%CE%91%CF%81%CF%87%CE %B9%CE%BC%CE%AE%CE%B4%CE%B7%CF%82.pdf
11. http://kotsanas.com/exh.php?exhibit=0204006
Bibliography
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Archimedes Physicist
https://el.wikipedia.org/wiki https://el.wikipedia.org/wiki/Αρχή_του_Αρχιμήδη https://www.arcmeletitiki.gr/ Εκπαιδευτική Ελληνική Εγκυκλοπαίδεια, τόμος Β’, Εκδοτική Αθηνών, pages 56-57 ▪ Η Ιστορία του Ελληνικού Έθνους, τόμος Ε’, Εκδοτική Αθηνών, pages 322-332
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Bibliography
Archimedes Engineer
1. A site for ancient greek inventions: http://kotsanas.com/gb/cat.php?category=07 2. Information about the siege of Syracuse: http://laonikos13galanis.blogspot.gr/2013/12/214-212.html 3. Kotsanas Kostas, Ancient Greek Technology - Inventions of the ancient Greeks, 2015,σελ. 128-131 4. Official website of Museum of Ancient Greek Technology, Kotsanas: http://kotsanas.com/ 36
5. Finally we would like to thank SlidesCarnival for the amazing templates they offer.
Students worked on this project: 1.
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3.
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Archimedes Astronomer: a. Tsakiridou Dimitra b. Seseri Konstantina c. Florou Paraskevi Archimedes Mathematician: a. Antoniadou Anni b. Mavropoulou Alexandra c. Mitsopoulou Maria Archimedes Physicist: a. Chatziioannou Lamprinos b. Gougousis Elias c. Fidanis Apostolos Archimedes Engineer: a. Panagiotidis Georgios b. Panagopoulos Konstantinos c. Tachtatzis Anastasios
Under the supervision of: Dr. Stavros Papadopoulos Dr. Claire Achilleos The students worked on the English version: Chatziioannou Lamprinos Tachtatzis Anastasios
Thank you for your attention! 1st Experimental High School Of Thessaloniki “Manolis Andronikos�
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