Calculating the Height of the Pyramid of Cheops

Thales of Miletus, with his astronomical knowledge, knew that in the region of Giza at a specific midday the sun shaped a 45° angle to the ground level (and went through the axis of the big pyramid). He stood in front of the pyramid, with his stick carved an arc with radius his height and waited for the moment when his shadow reached the arc. Then, as the length of his own shadow was equal to his height, so the height of the pyramid was equal to the length of its shadow. That is to say, the pyramid's height was equal to the sum of half the side of its base and length of its exceeding shadow. The method can also be used with the application of proportions with the creation of similar triangles. Then, as many times the shadow of the object is greater than the shadow of the stick, so many times is the object taller than our stick. SOURCES: “Proklos Diadochos, A Commentary on the First Book of Euclid's Elements”