By The Engineer, contributing writer for WonderfulEngineering.com
The one theorem that almost anyone who has ever studied Mathematics remembers is the Pythagoras’ theorem. It is the most well-known theorem for about 2,500 years now and has allowed the mankind to evolve in a myriad of ways. Its applications are limitless and range from construction to even evaluating the atomic structure of a crystal. However, up until now, it was bound to 2D only.
For the last 5 years, an aerospace and aeronautics engineer Luis Teia has been on a quest to understand the Pythagoras’ theorem in 3D. Using his paper, “Pythagoras triples explained via central squares” that was published in the 2015 edition of Australian Senior Mathematics Journal, he has derived the proof.
Okay, sounds amazing but what on Earth does it really mean? Before we jump into the details, the 2D proof of the theorem required about half a page, right? For the 3D proof, a book of 120 pages is required – that’s how complex it is. The geometrical part was drawn by making use of CAD and the algebra covers the 2/3rd of the book. Both, 2D and 3D, proofs are interconnected and the 3D proof is, in fact, built using the 2D one in a particular way.