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
They found it very hard to write down equations or number problems.

7. Greek mathematicians were very interested in proving that certain mathematical ideas were true.
They spent a lot of time using geometry to prove that things were always true,even thoughpeople like Egyptians and Babylonians already knew that they were true most of the time away.

8. 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
They found it very hard to write down equations or number problems.

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

11. 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

12. THALES He knew many number relations
In his work is the foundation of deductive geometry
He is credited with a few of the simplest propositions relating to the plane figures
His great contribution lay in suggesting a geometry of lines and in making the subject abstract
He gave the idea of a logical proof as applied to geometry

13. 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.

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

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

16. 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

17. 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

18. TV screen size is measured diagonally across the screen
TV screen size is measured diagonally across the screen. A widescreen TV has an aspect ratio of 16:9, meaning the ratio of its width to its height is 16/9. Suppose that a TV has a one inch boundary one each side of the screen. If Joe has a cabinet that is 34 inches wide, what is the largest size wide screen TV that he can fit in the cabinet?

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

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

21. 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

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

23. Plato (428 BC – 348 BC),
Philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western World.

24. Plato’s Cave Analogy

26. In Plato’s Divided Line, Mathematics falls under the following category:
Highest form of true knowledge
Second highest form of true knowledge
A form of belief, but not true knowledge
A form of perception

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

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

29. 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

30. HIPPOCRATUS PROBLEM
He proved that the lune bounded by the arcs labeled E and F in the figure has the same area as does triangle ABO

31. 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

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

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

34. The axiomatic method
The Elements begins with definitions and five postulates.
There are also axioms which Euclid calls 'common notions'. These are not specific geometrical properties but rather general assumptions which allow mathematics to proceed as a deductive science. For example:
“Things which are equal to the same thing are equal to each other.””

36. Euclid's fifth postulate cannot be proven from others, though attempted by many people.
Euclid used only 1—4 for the first 28 propositions of the Elements, but was forced to invoke the parallel postulate on the 29th.
In 1823,Bolyai and Lobachevsky independently realized that entirely self-consistent "non- Euclidean geometries" could be created in which the parallel postulate did not hold.

37. Our world is non Euclidean
Restate the fifth postulate: Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line.
Spherical geometry is just as real as Euclidean geometry, but the theorems and general results are very different. There are quite a few results from Euclidean geometry that are completely false in spherical geometry (and vice versa).

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

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

40. 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

41. LITERATURA Vladimir Devide: “Na izvorima matematike”
Dadić Žarko: “Povijest ideja i metoda u matematici i fizici”; ŠK, 1992.
http// hibit/exhibit/d- mathematics/Greek_math.html

42. Authors:
Ivana Pušić
Dajana Rudić
Ines Malić