In the last decade of Vespasian's rule, uprisings and disasters around Rome and the Roman Empire were bringing his fame as a ruler down to levels that he did not like. To help get the Roman peoples admiration and votes back, he decided to give them a present like no other with the money and riches gained from the Siege of Jerusalem and the Jewish Temple; a feat that would last over 2 millennia and rival the biggest stadiums in today's "modern" world. He gave them the Colosseum, otherwise known as the Flavian Theatre. A political statement, as well as a statement of the astounding technology that Roman builders possessed, the Colosseum has stood for nearly 2,000 years, and although not nearly in the perfect state it was in when built, it has not fallen prey to the elements. Today, very few architects, and engineers can actually replicate, or even describe the very complex techniques that went into the building of the structure. Part of the reason for this is that the actual architects and engineers who designed the building are unknown. Whoever it was used techniques refined over hundreds of years, and learnt from different cultures such as the Greeks, Egyptians, and Eastern Europe. The architect and engineers for the Colosseum made a structure that we as humans might never see again.
The Design and Engineering.
The Colosseum as a whole is an absolute masterpiece of design, and has set a sort of standard for arena design today. What looks like a simple oval shape, it is actually a very carefully planned out and thought of design. It was thought to be originally designed by combining two semi-circle theaters (like a classic Roman/Greek amphitheater) facing each other, however it is now more agreed on that the architect used techniques we use today, and are taught about in our math class: the Pythagorean triangle and inscribed circle scheme. This method involves first drawing a proper right triangle in the center of the site at the origin (if you were to draw an axis on the site, with the center being the origin) and then creating four other congruent triangles in each quadrant until you have a diamond shape.