GREEK MATHEMATICS
INTRODUCTION
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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
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FIRST – influenced by Pythagoras
SECOND – Plato and his school
THIRD – Alexandrian School flourished in
Grecian Egypt and extended its
influence to Sicily and Palestine
GREEK NUMBERS
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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)
Some other numbers in greek symbols
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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.
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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.
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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
MATHEMATICIANS
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Thales
Pythagoras
Anaxagoras
Democritus
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Aristotle
Hipocrates
Euclid
Archimedes
THALES (grč.
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Θαλής)
Born 624. BC in
Miletus
the first of the
Greeks who took
any scientific
interest in
mathematics in
general
Improved Egyptian
mathematics
THALES
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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
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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
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The ratios of any 2
segments on the first
line equals the ratios
of the according
segments on the
second line
THALES THEOREM
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If AC is a
diameter, then
the angle at B is
a right angle
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 )
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Born 460. BC, died
370.BC
Famous atomist
introduced the
idea of an infinite
number of points
that make up the
line
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He observed that a cone or pyramid has
one-third the volume of a cylinder or
prism 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. Ἀριστοτέλης )
Born 384. BC, died
322. BC
 Greek philosopher,
a student of Plato
and teacher of
Alexander the
Great
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For him the base of
mathematics is logic,
but the nature of
mathematical relations
is completely specified
by postulates that
dictates the physical
experience
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
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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. Εὐκλείδης )
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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
ELEMENTS
written about 300 B.C.
 textbook that includes number
theory
 the Euclidean algorithm for finding
the greatest common divisor of
two numbers
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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 "nonEuclidean 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).
ARCHIMEDES (grč. Ἀρχιμήδης)
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mathematician and
inventor born 287.
BC in Syracuse
founder of
quantitative physics
as a
mathematician,
advocate of logical
processes
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He determined approximate
values of some irrational
numbers
1351/780>
>265/153
28/7> π >223/71
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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
LITERATURA
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Vladimir Devide: “Na izvorima
matematike”
Dadić Žarko: “Povijest ideja i metoda
u matematici i fizici”; ŠK, 1992.
http//www.ibilio.org/expo/vatican.ex
hibit/exhibit/dmathematics/Greek_math.html
http://www.historyforkids.org
Authors:
Ivana Pušić
Dajana Rudić
Ines Malić