Mathematics defines architecture; without it there would be no ancient architecture left standing. It had to be balanced or it would not have stood the tests of time. Finding Math in Ancient Architecture sounds as if students are to snoop around and discover that ancient buildings are nothing more than enlarged calculating machines. This could be a possibility if all were to travel to distant lands where some of these old buildings are, or at least finding rebuilt copies of them.
Getting to where their dimensions could be assessed and come to some conclusion is too time consuming and is not practical. The world today does not have the time to follow their whims, even if its citizens could afford the expense. The next best thing is imagine, to visualize,+ and to think. And if that doesn't work to listen in to others on the Internet to see how they would manage such a question.
From history and from art classes it can be learned that the Parthenon in Greece was built with a slight dip in the center so that when viewed it would appear to be straight and not seen in a slight contorted perspective. The architect that drew up that blueprint must have had a few straight lines strapped to his sandals.
The kinds of buildings Egyptians built look more like the Phoenician alphabet than Roman Numerals; can't you just hear your three year old shouting with glee on first sighting one, look daddy, an A.
While trudging on in the hot sand with the sun beaming down travelers could take a swig of water from their pouch and this brings you back to reality and to the fact your son is at home, not far, far, away. You have been a little out of your head. Recovering, you decide to make the most of your delightful delusion, and answer "Yes, son and over there, while pointing at a ziggurat, is a Z. of course, this is not a ziggurat but a step pyramid, but the principle is the same, isn't it?
Well now you are not sure where in the world you are, in Egypt, or somewhere in Mexico or Guatemala. But wherever you are you know they don't make buildings like that anymore. Seriously, most ancient architects were also mathematicians. Justinian, a 6th century Byzantine emperor, hired two mathematicians to construct the Hagai Sophia, a masterful work of Byzantine architecture, now used as a museum in Istanbul, Turkey.
Another great mathematician, Pythagoras, said all things were numbers. Yes he's the one that gave the world the famous rule concerning the sides of a triangle, known as the Pythagorean Theorem. It is: "A proved geometric proposition stating that the square of the longest side hypotenuse of a right triangle is equal to the sum of the squares of the other two sides".
He was also a musician and much of his discovery came about because of his observances of the distances between the length of musical bars and the timing of the music. He noted that placing notes equal distances from each other in certain sequences resulted in harmonious sounds. And, relating this to architecture, it created beautiful music.
A separation between architecture and mathematics occurred in the 19th century. Although a few stragglers still dabbled in both. One in particular, Buckminster Fuller, (1895-1983) 1983 from Massachusetts is known for his innovative lightweight structures that are based on mathematics. He named his invention energetic-synergetic geometry. These constructions made the best use of space, and were designed to be primarily used and not necessarily for show and tell.
So yes, there is mathematics in architecture, just ask any three years old who has discovered the fun of playing with blocks. One, two, three, four, five, oops, the house fell down. But one day he will figure it out. The weight must be equally distributed. The biggest problem now is 'can he wait?'