Building a Pyramid

I promised my little brothers that I would put some pictures of the pyramid I built in Minecraft up on my blog, so here they are.

View of the pyramid from the south, along the entrance causeway.

This pyramid was actually a pretty interesting learning experience. Minecraft takes place in a world of blocks, which are usually taken to be one meter on a side. When I decided to build a pyramid, I first thought of building a replica of the Great Pyramid of Giza, which is 230.4 meters (755.9 feet) on a side at the base and would have stood 146.5 meters (480.6 feet) tall when it was built. Given the constrictions of Minecraft my pyramid would need to have a 45\(^\circ\) angle rather than the 51\(^\circ\) 50' 40" of the actual one (and thus only 115 meters high), and a quick calculation showed that it would require on the order of 2,054,360 blocks to build an entire pyramid.

Edit (6/14/13): The calculation is simple; it's just
\[N=\sum_{n=1}^{115}(2n)^2\] which can be solved in four lines of Python code, viz:
>>> N = 0
>>> for n in range(1, 116):
...    N += (2 * n)**2
>>> print(N)

View of the pyramid from the south-east corner. Ignore the flying castle in the background.

I also quickly learned that the area I wanted to build it in was much too small, so I decided to scale down and build a smaller pyramid 100 meters on a side. The same calculation showed that such a pyramid would still require 171,700 blocks (same calculation as before with different upper limit), and since I was going to have to gather every single block myself, I decided to cheat and take advantage of Minecraft physics (or lack thereof) to build a hollow pyramid consisting of only an outer shell.

View from atop the black obsidian pyramidion. Some previous work can be seen, the Library building to the left and the floating Sky Castle to the right.

This scheme still required a total of 10,000 blocks of sandstone, which I methodically went about gathering. (Edit (6/14/13): To arrive at that number, imagine the pyramid as a series of concentric square rings, since it's hollow. You can imagine collapsing them down into each other, until you have nothing but a square patch of sandstone a hundred meters on a side. Simply square that number, and you arrive at 10,000.) The entire process of gathering materials and building the pyramid probably took me a good ten hours over a period of several days, and really put into perspective what it must have taken to build an actual, solid pyramid over twice as large as the one I finally completed.

The Sun rising behind the pyramid in the east. It is very impressive in-game.