English: Computing the height of the Great Pyramid of Giza using a stick and the lengths of the shadows on the floor. An illustration of the geometric intercept theorem, attributed to Thales.

Height of the Cheops Pyramid

According to some historical sources the Greek mathematician Thales applied the intercept theorem to determine the height of the Cheops' pyramid. The following description illustrates the use of the intercept theorem to compute the height of the Cheops' pyramid. It does not however recount Thales' original work, which was lost.

Thales measured the length of the pyramid's base and the height of his pole. Then at the same time of the day he measured the length of the pyramid's shadow and the length of the pole's shadow. This yielded the following data:

• height of the pole (A): 1.63m
• shadow of the pole (B): 2m
• length of the pyramid base: 230m
• shadow of the pyramid: 65m

From this he computed

${\displaystyle C=65m+{\frac {230m}{2}}=180m}$

Knowing A,B and C he was now able to apply the intercept theorem to compute

${\displaystyle D={\frac {C\cdot A}{B}}={\frac {1.63m\cdot 180m}{2m}}=146.7m}$