greek math 123345456546

 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 ins

GREEK MATHEMATICS

 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

 SECOND – Plato and his school

 THIRD – Alexandrian School flourished in

Grecian Egypt and extended its influence to Sicily and Palestine

 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)

GREEK NUMBERS

Some other numbers in greek symbols

 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

 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

 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

MOST FAMOUS GREEK

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

 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

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

INTERCEPT THEOREM

segments on the first

line equals the ratios

of the according

segments on the

second line

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

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

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?

SQUARE NUMBERS

 These numbers are

clearly the squares

of the integers 1, 4,

9, 16, and so on

Represented by a square of dots

PYTHAGORAS AND MUSIC

 musical notes could be translated

into mathematical equations

DEMOCRITUS (grč Δημόκριτος )

 Born 460 BC, died 370.BC

 He observed that a cone or pyramid has third the volume of a cylinder or prism

one-respectively with the same base and height

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

Plato’s Cave Analogy

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

ARISTOTLE (grč. ριστοτέληςἈ )

 Born 384 BC, died

322 BC

 Greek philosopher, a student of Plato and teacher of Alexander the Great

 For him the base of

mathematics is logic, but the nature of mathematical relations is completely

specified by postulates

that dictates the physical experience

of medicine

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

EUCLID (grč Ε κλείδης ὐ )

 Born 300 BC

 pioneer of axiomatics in

geometry

 His work Elements

fundamental work in the

 written about 300 B.C

 textbook that includes number theory

 the Euclidean algorithm for finding the greatest common divisor of two

numbers

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

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.””

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

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).

 He determined approximate values

of some irrational numbers

1351/780> >265/153

28/7> π >223/71

 A sphere has 2/3 the

volume and surface

area of its

circumscribing cylinder

were placed on the

tomb of Archimedes at his request

Ivana Pušić Dajana Rudić Ines Malić