HOW DID TALES DETERMINE THE HEIGHT OF A

PYRAMID

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

100 000 people built this pyramid for 20 years

It is 146 m high During time it lost 10 meters of its

original height

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

It is an area as big as 10 football playgrounds.

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.