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GREEK MATHEMATICS

GREEK MATHEMATICS. INTRODUCTION. The beginnings of Greek mathematics originated from the 6th century BC to the 5th century AD The word mathematics comes from the Greek word μάθημα (mathema), meaning "subject of instruction “. PERIODS IN GREEK MATHEMATICS. FIRST – influenced by Pythagoras

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GREEK MATHEMATICS

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  1. GREEK MATHEMATICS

  2. INTRODUCTION • The beginnings of Greek mathematics originated from the 6th century BC to the 5th century AD • The word mathematics comes from the Greek word μάθημα (mathema), meaning "subject of instruction“

  3. PERIODS IN GREEK MATHEMATICS • FIRST – influenced by Pythagoras • SECOND – Plato and his school • THIRD – Alexandrian School flourished in Grecian Egypt and extended its influence to Sicily and Palestine

  4. GREEK NUMBERS • Greeks had a variety of different ways of writing down numbers • Some Greeks used a system based on writing the first letter of the word for that number • For number ten “Deka”, they would draw a D to mean 10. (a delta, in the Greek alphabet)

  5. Some other numbers in greek symbols

  6. Because the Greeks had very clumsy ways of writing down numbers, they didn't like algebra • They were more focused on geometry, and used geometric methods to solve problems that you might use algebra for

  7. MOST FAMOUS GREEK MATHEMATICIANS • Thales • Pythagoras • Anaxagoras • Democritus • Aristotle • Hipocrates • Euclid • Archimedes

  8. THALES(grč.Θαλής) • Born 624. BC in Miletus • the first of the Greeks who took any scientific interest in mathematics in general • Improved Egyptian mathematics

  9. PROPOSITION RELATING PLANE FIGURES • a circle is bisected by its diameter, • the angles at the bases of any isosceles triangle are equal • if two straight lines cut one another, the opposite angles are equal. • if two triangles have two angles and a side in common, the triangles are identical.

  10. INTERCEPT THEOREM • The ratios of any 2 segments on the first line equals the ratios of the according segments on the second line

  11. THALES THEOREM • If AC is a diameter, then the angle at B is a right angle

  12. PHYTAGORAS (grč.Πυθαγόρας) • Born 570. BC in Samos • Died 495. BC • worked with abstract geometric objects and numbers • gathered his school as a sort of mathematician secret brotherhood

  13. PHYTAGORAS THEOREM • in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse

  14. SQUARE NUMBERS • These numbers are clearly the squares of the integers 1, 4, 9, 16, and so on. Represented by a square of dots

  15. PYTHAGORAS AND MUSIC • musical notes could be translated into mathematical equations

  16. DEMOCRITUS(grč.Δημόκριτος) • Born 460. BC, died 370.BC • Famous atomist • introduced the idea of an infinite number of points that make up the line

  17. He observed that a cone or pyramid has one-third the volume of a cylinder or prism respectively with the same base and height

  18. ARISTOTLE (grč.Ἀριστοτέλης) • Born 384. BC, died 322. BC • Greek philosopher, a student of Plato and teacher of Alexander the Great

  19. For him the base of mathematics is logic, but the nature of mathematical relations is completely specified by postulates that dictates the physical expirience

  20. HIPPOCRATES (grč. Ἱπποκράτης ) • Lived from 460. BC to 377. BC • an ancient Greek physician and was considered one of the most outstanding figures in the history of medicine

  21. HIPPOCRATUS PROBLEM • moon of the side of a square inscribed in a given quarter circle is equal to the square of the given

  22. EUCLID (grč.Εὐκλείδης) • Born 300. BC • pioneer of axiomatics in geometry • His work Elements fundamental work in the field of Greek mathematics • influenced the development of mathematics in the next 20 centuries

  23. ELEMENTS • written about 300 B.C. • textbook that includes number theory • the Euclidean algorithm for finding the greatest common divisor of two numbers

  24. the first edition of the translation from Arabic into Latin 1482.

  25. ARCHIMEDES (grč.Ἀρχιμήδης) • mathematician and inventor born 287. BC in Syracuse • founder of quantitative physics • as a mathematician, advocate of logical processes

  26. He determined approximate values of some irrational numbers 1351/780> >265/153 28/7> π >223/71

  27. A sphere has 2/3 the volume and surface area of its circumscribing cylinder • A sphere and cylinder were placed on the tomb of Archimedes at his request

  28. LITERATURA • Vladimir Devide: “Na izvorima matematike” • Dadić Žarko: “Povijest ideja i metoda u matematici i fizici”; ŠK, 1992. • http//www.ibilio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html • http://www.historyforkids.org

  29. Authors: Ivana Pušić Dajana Rudić Ines Malić

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