ABSTRACT:
We present here an unusual example where a simple geometric theorem emerges from a complex mechanism. Even if the reader is familiar with the Pythagorean theorem [1-3] and how to calculate the area of a circle, this example may provide a little surprise. We have utilized a basic rule from mechanics, that two points on any arbitrarily moving rigid body always remain at a fixed distance apart, and their relative motion is always tangential and never radial [4]. We have also utilized a basic planetary phenomenon that Earth must complete 366 rotations about its axis when circling around the Sun in 365 days [5]. That is because, one additional rotation about its axis must be completed for going around the Sun, with reference to a fixed reference such as a distant star. Likewise, with reference to a fixed reference, the Moon must complete one rotation about its axis when going around Earth, although the near side of the Moon remains towards Earth during the motion.