greek math 123345456546

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
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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

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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.






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
MATHEMATICIANS





Thales
Pythagoras
Anaxagoras
Democritus






Aristotle
Hipocrates
Euclid
Archimedes



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




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


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


The ratios of any 2
segments on the first
line equals the ratios
of the according
segments on the
second line


THALES THEOREM


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 )





Born 460. BC, died
370.BC
Famous atomist
introduced the idea
of an infinite number
of points that make
up the line




He observed that a cone or pyramid has onethird 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