Shadow calculation is a technique used to measure the height of an inaccessible object (particularly buildings) by measuring the length of the shadow cast by the object. The technique used dates back to ancient Greece, when the Greek mathematician Thales visited Egypt and surprisingly measured the height of the Great Pyramid.
The story begins with Thales’ visit to Egypt, where the Great Pyramid is located. He was amazed by the beauty of the Great Pyramid, and as he climbed to the top of the pyramid, he posed a question “How tall is the pyramid?”
No one at the time can answer him, as no one has ever cared about his height. Maybe the builder got the answer, but that was about 2,000 years ago, and since then no one cares about height. No one can measure the height of such a giant from the bottom up.
Disappointed, Thales said, “Don’t bother with my question, I knew the answer!” Everyone around him was shocked and petrified. Everyone sees their shadow as the Sun’s projection of themselves onto the ground, but what Thales sees is an abstract triangle formed by the top and bottom of the object, and the end of the shadow. Thales realized that there is a proportion in these abstract triangles, and Thales showed that they are 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 proportions, and therefore the proportion of the abstract triangle also changes in the same way. He did experiments observing the pyramids in the desert and proves that he is right. His result amazed all his people in his time.
In optics, the distance from the Sun is assumed to be infinite, and therefore the Sun’s rays can be considered as parallel rays. By placing a stick near the object we want to measure, we can tell pretty well that the shadow cast by the stick and the object share the same angle. Therefore, using similar trigonometry, we will get the desired result.
Trigonometry has been applied and today this technique is called shadow calculus and has been widely used to measure the height of different objects. By another means trigonometry can be used to get the different variables depending on the situation, for example Sundial is a method used to get the local time zone precisely by casting the shadow of an object. Similarly, we can even get the GPS location of an object, as long as it is the length of the shadow, the height of the object, and the local time zone.