1. By: Ines Burazin Tomislav Haršanji Igor Sušić Matea Ugrica
Greek mathematics
By: Ines Burazin
Tomislav Haršanji
Igor Sušić
Matea Ugrica

2. Introduction: from the 7th century BC to the 4th century AD
around the shores of the Mediterranean
word "mathematics" – from the ancient Greek μάθημα (mathema) = "subject of instruction“
influences: Babylonian  and  Egyptian  civilizations 
differences:
respect of geometry and the idea of formal proof

3. Introduction: achievements: two periods: ideas on number theory
mathematical analysis
applied mathematics
approached close to integral calculus
two periods:
Classical
Hellenistic (4th century BC)

4. Greek numeral system known as Attic or Herodianic numerals
fully developed by about 450 BC
in regular use possibly as early as the 7th Century BC
it is a base 10 system 

5. The Three Classical Problems

6. Squaring the circle
It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.

7. Doubling the cube also known as the Delian problem
impossible to solve, because   ≈ is not a constructible number
double the size of the altar for Apollo, which was a regular cube

8. The trisection of an angle
involves the solving of a cubic equation
something that cannot be done
90° can be trisected
a general angle cannot (example 60°)

9. Famous Greek Mathematicians
THALES
PYTHAGORAS
ZENO OF ELEA
EUCLID
ARCHIMEDES
ERATOSTHENES

10. Thales of Miletus
“The most difficult thing in life is to know yourself.”

11. Thales of Miletus the first of the seven wise men of Greece
used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore
first person known to have studied electricity
died at 78 in the 58th Olympiad (548–545)

12. Propositions A circle is bisected by any diameter.
The base angles of an isosceles triangle are equal.
The angles between two intersecting straight lines are equal.
Two triangles are congruent if they have two angles and the included side equal.
An angle in a semicircle is a right angle.

13. Pythagoras
“We ought so to behave to one another as to avoid making enemies of our friends, and at the same time to make friends of our enemies.”

14. Pythagoras
called Pytha-goras because the Pythian oracle predicted his birth
known as “the father of numbers”
Pythagoras and his students believed that everything was related to mathematics
everything could be predicted and measured in rhythmic patterns or cycles.

15. Figurate Numbers
Numbers geometrically constructed had a particular importance to the Pythagoreans.
Triangular numbers. These numbers are 1, 3, 6, 10, The general form is the familiar n=n(n+1)/2
Square numbers These numbers are clearly the squares of the integers 1, 4, 9, 16, and so on. Represented by a square of dots
the well known formula (2n − 1) = n2.

16. Pythagorean spiral

17. Zeno of Elea Zeno's paradoxes: "Achilles and the Tortoise"
"Arrow paradox"

18. Zeno's paradoxes
paradoxes of Achilles and the Tortoise

19. Euclid
“There is no royal road to geometry.”

20. Euclid nobody knows much about Euclid's life anymore
often referred to as the "Father of Geometry“

21. Euclid Five works by Euclid have survived to our day:
1. The Elements - The Elements can be topically divided into four sections:
Books I-VI — Plane geometry
Books VII-IX — Theory of Numbers
Book X — Incommensurables
Book XI-XIII — Solid Geometry
2. Data - includes geometric methods for the solution of quadratics.
3. Division of Figures
4. Phaenomena - on spherical geometry,
5. Optics

22. Euclid’s theorem
b² = a · m
c² = a · n

23. Euclid

24. Archimedes
“Eureka!” “Give me the place to stand, and I shall move the earth.” “Do not disturb my circles!”

25. Archimedes from Syracuse
the most famous and probably the best mathematician of antiquity
made many discoveries in mathematics and physics

26. The Golden Crown
used his principle of buoyancy to determine whether the golden crown was less dense than solid gold

27. The Burning Mirror (Glass)

30. Eratosthenes
born in Cyrene
 invented the armillary sphere 

32. Eratosthenes' other contributions include:
The measurement of the Sun-Earth distance, now called the astronomical unit.
The measurement of the distance to the Moon.
The measurement of the inclination of the ecliptic with an angle error of 7'. 
He compiled a star catalogue containing 675 stars, which was not preserved. 
A map of the Nile's route as far as Khartoum. 
A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia. 

33. Thank you for your time!