This is the famous Bent Pyramid. The lower part of the pyramid has an angle of 54° and the upper part is at 43°. Why is it bent? Really, who knows. The two likely reasons are:Time or money (well isn’t time = money). Basically this idea says that they either didn’t have the time or money to finish the pyramid at the initial slope. To cut costs (or time) they changed the angle. Building the pyramid at the original slope caused structural instabilities. Either the foundation couldn’t take the weight or the building material itself started to crack.
I don’t really have anything to add to the debate about which theory is more likely (though I do find it quite interesting). Oh, then there is the theory that the aliens that give the Egyptians pyramid building technology played a practical joke on them causing the pyramid to end up bent.
The second reason is interesting to me. How tall of a pyramid can you build? What is the best angle? Let me assume that indeed there are structural problems with the material and look at two ways of thinking about the limiting height.
How tall can I make a column of stone?