82 GREEK MATHEMATICS

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






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


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




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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


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
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