ARCHIMEDES’ LIFE AND WORK IN PHYSICS, ENGINEERING, ASTRONOMY AND MATHEMATICS
A. Biography 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. He lived at Syracuse, a Greek Colony in Sicily, Southern Italy, where he spent most of his life and in Alexandria, in Northern Egypt, where he studied at the Great Library and met other leading minds of his era such as Conon of Samos and Eratosthenis of Cyrene. 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. B. Astronomy 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. 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. 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. 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. Of course, what we mentioned above is not enough to characterize Archimedes an astronomer. He did much more than that. 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. 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.
C. Mathematics His work on circles: 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 accurate calculation of π. 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 multiplied by the square of its radius.
His work on circles is considered so great that this specific type of circle has been named after him (Archimedean Circle). 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: 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 ¼.
Spheres and cylinders: 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. Plutarch in “ Parallel Lives” said that “He(Archimedes) placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life”.
D. Physics
“Eureka” undoubtedly holds a position among the most well-known phrases worldwide and is directly connected to Archimedes’ most important achievement in Physics. It is related to the Archimedes’ Principle. The story behind this principle is, that, 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 used to determine the volume.
Archimedes’ experiment 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”. Applications of his principle in everyday life can be seen in Shipbuilding, Submarines , that need to constantly change their flotation values in order to reach greater depths or to return to the surface, Diving. 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: 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.
E. Engineering Archimedes also made a lot of contributions in engineering. During the Siege of Syracuse(213-212 BC), he invented a lot of defense systems in order to protect his city. The “Iron hand”: 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. This distant ancestor of the modern crane was used against enemy ships, that tried to conquer Syracuse. The iron hand
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.
Steam cannon
Archimedes’ screw: 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.
Archimedes' screw Uses of Archimedes’ inventions in our daily life: Archimedes’ screw used to drain poldgers from a lake in Netherlands or a modern crane designed like the “Iron hand”, but for different purpose.
Bibliography For Archimedes as an Astronomer: 1. https://el.wikipedia.org/wiki/%CE%91%CF%81%CF
%87%CE%B9%CE%BC%CE%AE%CE%B4%CE%B7%CF %82 2. http://www.academy.edu.gr/Antikythera-Digital-BookFiles/VI_ALL_185_200.pdf
3. https://www.britannica.com/biography/Archimedes 4. http://www.newworldencyclopedia.org/entry/Archimedes 5. https://www.arcmeletitiki.gr/images/uploads/pdf/arc_arx 6. 7. 8. 9. 10.
11.
▪ ▪ ▪ ▪ ▪ 1. 2. 3. 4. 5.
5.pdf http://www.mathlab.upatras.gr/wpcontent/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/wpcontent/uploads/2013/09/%CE%91%CF%81%CF%87%CE %B9%CE%BC%CE%AE%CE%B4%CE%B7%CF%82.pdf http://kotsanas.com/exh.php?exhibit=0204006
For Archimedes as a 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 For Archimedes as an Engineer: A site for ancient greek inventions: http://kotsanas.com/gb/cat.php?category=07 Information about the siege of Syracuse: http://laonikos13galanis.blogspot.gr/2013/12/214-212.html Kotsanas Kostas, Ancient Greek Technology - Inventions of the ancient Greeks, 2015,σελ. 128-131 Official website of Museum of Ancient Greek Technology, Kotsanas: http://kotsanas.com/ Finally we would like to thank SlidesCarnival for the amazing templates they offer. Students worked on this project: Archimedes Astronomer: Tsakiridou Dimitra Seseri Konstantina Florou Paraskevi Archimedes Mathematician: Antoniadou Anni Mavropoulou Alexandra Mitsopoulou Maria Archimedes Physicist: Chatziioannou Lamprinos Gougousis Elias Fidanis Apostolos Archimedes Engineer: Panagiotidis Georgios Panagopoulos Konstantinos
Tachtatzis Anastasios Under the supervision of: Dr. Stavros Papadopoulos Dr. Claire Achilleos Students worked on the English version: Chatziioannou Lamprinos Tachtatzis Anastasios