The document describes the Keops pyramid located near Cairo, Egypt, which was built approximately 4,500 years ago as the tomb of the pharaoh Khufu and his wife. It discusses how Thales of Miletus, an ancient Greek philosopher, used geometry to measure the height of the pyramid by comparing the lengths of shadows at different times of day. Later, students were able to use GeoGebra software to more easily determine the surface area and volume of the pyramid.

2. 
It is placed in Giza near Cairo (Egypt)
It represents one of the SEVEN WONDERS OF
THE WORLD
It was built 4500 years
ago to be the tomb
of pharaoh
and his wife
KEOPS PYRAMID

3. 
100 000 people built this pyramid
for 20 years

4. It is 146 m high
During time it lost 10 meters of its original
height

5. KEOPS PYRAMID
The Great
Pyramid was
the highest
building in
the world, till
the Eifel
Tower was
built in 1887

6. The inside of the pyramid contains
2 300 000 stone blocks each of them
weights 2.5 tons ( the mass of a jeep)

7. 
The base of the pyramid has the
shape of a square, which length is
233 m so that the pyramid covers
the area of 5.4 acres

8. It is an area as big as 10 football
playgrounds.

9.  He lived from 624 to 547 BC.
 He was considered to be the „Father of Greek Philosophy”.
Thales decided to
measure , what
was considered to
be immeasurable
at those times

10. His conclusion:
When the length of his shadow equals his
height,
than the length of the pyramid equals the
height of the pyramid!
Pyramid
Thales
Suns rays are concurrent !
Length of
Thales ‘
shadow
Thales
Height =
Length of the
pyramid’s
shadow
Height of
pyramid =

11. General conclusion:
How many times men’s height is bigger or
smaller than the length of the shadow,
that times is the height of the pyramid bigger or
smaller of the length of the shadow !
Pyramid
Thales
Suns rays are concurrent!
The lenght
of Thales’
shadow
Thales
heigh :
The lenght of
the pyramid’s
shadow
The height
of the
pyramid
: =

12. The problem which appeared:
How to measure the length of a pyramid shadow,
if one part has to be measured in the inside of the
pyramid?
Pyramid
Thales
Shadow of a
pyramid
Thales’
shadow

13. Of course, Thales solved also this problem:
a
2
__ We measure
this
Sun’s ray
When the interrupted becomes concurrent to the
edge of the base,
Concurrent!
part of the shadow inside the pyramid
will be as long as the half length of the base.
We can easily measure the outer part
of the shadow!
As the shadow of the pyramid moves (because of Sun),
so moves the interrupted line
that determines the length of the shadow.

14. Thales had to work out many details like :
- His height
- The length of his shadow
- The length of the pyramid s shadow
to determine the height of the pyramid
a
2
__ We measure
this
Sun’s ray

15. 
We, the students of Primary
School Mikleuš, have much
easier and faster determined
the surface area and the
volume of the Keops pyramid
by using GeoGebra.