Are there any examples of conical shaped pyramids built by ancient peoples, and if not, I wonder why?
Not that I know of. I know the reason that the Egyptians built square based pyramids was probably as follows. You start with a simple square based one storey building. It is the easiest structure to build. They’re called mastabas. Sometime later some smart alec says “Hey let’s put another storey on top of that one!” and realises the structure will be more stable if you make the second storey smaller (uniform width/depth towers are not as easy). And the again for a third story until you get a step pyramid. This is exactly what happened in Egypt. http://en.wikipedia.org/wiki/Step_pyramid This is the easiest way yo build a multi storey structure. Later the great Snefru came along and said “wouldn’t that be great if the sides were not stepped but smooth?” and went on to build the first true pyramids. http://en.wikipedia.org