HOW DID TALES DETERMINE THE HEIGHT OF A PYRAMID
Aug 03, 2015
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
KEOPS PYRAMID
The Great Pyramid was the highest building in the world, till the Eifel Tower was built in 1887
The inside of the pyramid contains 2 300 000 stone blocks each of them weights 2.5 tons ( the mass of a jeep)
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
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
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
=
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
: =
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
a = 233 m
Of course, Thales solved also this problem:
a2__ 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.
a = 233 m
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
a2__ We measure
this
Sun’s ray
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.