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Euclid project


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Euclid's Elements was considered as the foundation of Mathematics till the end of 19th century. Is there a connection with his period and Alexander the Great's eastward battles ? Is there any possibility that the origin of his thought and the principles itself was from the Indian subcontinent ?

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Euclid project

  1. 1. Who is Euclid?
  2. 2. Euclid of Alexandria"Euclid" is the Greek name, meaning "Good Glory".Euclid - 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry".He was active in Alexandria during the reign of Ptolemy I (323–283 BC).His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.
  3. 3. Surviving FragmentsOne of the oldest surviving fragments of Euclids Elements, found atOxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagramaccompanies Book II, Proposition 5.
  4. 4. Euclids lifeLittle is known about Euclids life, as there are only a handful of references to him. It is believed that Euclid may have studied at Platos Academy in Athens.King Ptolemy asked if there was a shorter path to learning geometry than Euclids Elements, "Euclid replied there is no royal road to geometry.“Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought."
  5. 5. Painting HistoryEuclid in Raphaels School of Athens
  6. 6. Elements and EuclidAlthough many of the results in Elements originated with earlier mathematicians, one of Euclids accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics even today.The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.
  7. 7. Euclid through pictures
  8. 8. Elements and number theoryThe Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclids lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
  9. 9. Euclid through pictures
  10. 10. Euclidean geometryThe geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non- Euclidean geometries that mathematicians discovered in the 19th century.
  11. 11. DodecahedronEuclids construction of a regular dodecahedron
  12. 12. Other works of EuclidAt least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.1. Data: deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.2. On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
  13. 13. Other works of Euclid..3. Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution to Euclid is doubtful. Its author may have been Theon of Alexandria.4. Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.5. Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal."
  14. 14. CriticsHis (Euclid) definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious. (Bertrand Russell, The Teaching of Euclid, The article appeared in The Mathematical Gazette in 1902. The Nobel Prize in Literature 1950)Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture. (Bertrand Russell)
  15. 15. Poem about Euclid
  16. 16. Further researchAlexander the Great founded some twenty cities that bore his name, most notably Alexandria in Egypt. Alexander died in Babylon in 323 BC.Alexander crossed the Indus and fought and won an epic battle against King Porus (Purushottama), who ruled a region in the Punjab, in the Battle of the Hydaspes in 326 BC. Alexander was impressed by Poruss bravery, and made him an ally.In the aftermath of Alexanders conflicts in North-Western India, Megasthenes Herakles who travelled to India as the ambassador of the Seleucids during the reign of Chandragupta Maurya.
  17. 17. Further research..Dionysius was a Greek of the 3rd century BCE, who was sent as ambassador to the court of the Indian emperor Ashoka, by Ptolemy Philadelphus.He was preceded in this role by Megasthenes, ambassador to Chandragupta Maurya, and Deimachus, ambassador to his son, and father of Ashoka, Bindusara.It is possible that these Ambassadors, led by scholars from the ancient Greek empire, learned from the Indian Universities / Scholars and transferred our ancient wisdom (including Surgery from Ayurveda, Matahematics from Jyothisha and Philosophy from the Vedas) which later became the ancestral property of the Western world.
  18. 18. Project work• Compiled by Mrs. Sreeja MK, student of Teachers Education (B.Ed.) Programme 2011-12, Mahathma Gandhi University, 0481 – 2 393 120• Mahatma Gandhi University College of Teacher Education, Kudamaloor, Govt.High School Campus, Kudamaloor, Kottayam, Tel.No. 0481 – 2 391 264.