How Did Thales Measure a Pyramid?
How do you measure something enormous without climbing to the top?
The Answer
Ancient writers say Thales of Miletus used shadows. A known object and its shadow can reveal the height of a much larger object.
How Did It Work?
Place a vertical stick beside the pyramid. The stick and its shadow form one triangle; the pyramid and its shadow form another. Because the Sun reaches both at the same angle, the triangles are similar.
If a 1-metre stick casts a 2-metre shadow and the pyramid’s shadow is 280 metres, the pyramid is about 140 metres high.
History or Legend?
Ancient sources agree that Thales used shadows, but they do not describe the method in exactly the same way. The geometric idea is clear: measure indirectly when direct measurement is impossible.
Try It Yourself
Use a stick of known height to estimate a tree, flagpole, or building. Measure both shadows and use the same proportion.
From Voices of the Past: Origins
Sometimes all mathematics needs is a pyramid, the Sun, and a shadow.