Shadow Reckoning

Shadow reckoning is a technique used to measure the height of an inaccessible object (particularly buildings) by measuring the length of shadow the object casts. The technique used dates back to ancient Greek, when Greek mathematician Thales visitied Egypts and surprisingly measure the height of The Great Pyramid.

The story begin with the visit of Thales to Egypts, where lies the Great Pyramid. He was amazed by the beauty of the Great Pyramid, and as he ascends to the tip of the pyramid, he proposed a question “How high is the pyramid??”

Nobody at his time can answer him, as nobody has ever concern on its height. Perhaps the builder acquired the answer, but that was about 2000 years ago, and nobody bothers the height of it since then. Nobody can ever measure the height of such a giant from bottom to top.

Being disappointed, Thales said “Don’t bother my question, I knew the answer!” Everyone around him was shocked and petrified. Everybody sees their shadow as just the projection of themselves to the ground by the Sun, but what Thales see, is abtract triangle formed by both tip and bottom of the object, and the end of the shadow. Thales realized that there’s a proportion in these abtract triangles, and Thales proved that they’re similar and congruent, solving the problem to measure the height of The Great Pyramid.

Thales was so convinced that as the Sun moves, all angles, shadows will change in similar proportion and so the abstract triangle proportion changes in the same manner as well. He did experiments by observing the pyramids in the desert, and prove himself right. His result astounded all his people at his time.

In optics, the distance of the Sun is assumed to be infinity, and hence the rays from the Sun can be considered as parallel rays. By putting a stick near the object we wished to measure, we can fairly well say that the shadow cast by both stick and the object shares the same angle. Hence by using similar trigonometry, we’ll obtain our desired result.

The trigonometry has been applied and in modern days, this technique is called shadow reckoning, and been widely used to measure height of different objects. By further mean, trigonometry can be used in a way to get the different variables depending on situation, for instance Sundial is a method used to obtain local timezone precisely by projecting shadow of an object. Similarly, we can even obtain the GPS location of an object, provided it’s shadow length, object’s height as well as local timezone.