Thats a nice theory ;)
We can clearly see that there are sections, like a Giant Space Pizza.... but the Four Quarters are more clearly marked out as far as the Thickness of those Lines/Path. And these Paths seem to lead directly to the 4 Large Statues surrounding the Hanger
So thanks to your noticing those Statues we have 192 such Statues and 4 Larger Ones in the Center.
Who knows what the Purpose is, and the some kind of Time theory is a interesting one to ponder.
However if we look at it in another way to WHY build these Statues on top of those Columns, we maybe have to look at why Many Ancient Cultures on Earth did the same.
This usually is to represent Important Figures within History, for their Deeds/Accomplishments, their Rank/Importance etc. And so why would Statues be built to reflect a Culture.
Indeed it could be to showcase their entire Species/Culture, but maybe it could be also to represent individuals or events.
We on Earth make such Monuments to the Following, Rulers/Kings, Political Figures, Religious Leaders or people of Religious importance. Monuments to those who had a great effect on Culture and Mankind by their Arts (Musicians, Artists, Poets) or for their Deeds, such as Sacrificial deeds for the greater Good of their Culture, which include Military Personnel or people who had made a great impact on their people for various reasons, from people like Mother Teresa (And other Saints). Or people like Mahatma Gandhi and Nelson Mandela
As the Engineers do like to make Statues to signify importance of their kind, but are these Statues dedicated the their Culture as a Whole... or individuals?
I wonder if the Arena thus is to celebrate certain individuals at certain times in their Culture.
What if as i have speculated for a while, since the movie came out the whole Hanger has a Sacrificial Purpose and this place is where Sacrificial Engineers are taken from.... and in Return for their Sacrifice they receive Monuments Built in their Image with their Names Engraved so their Sacrifice is never forgotten and they are Immortalized in Stone.