Calculate Stones in a Step Pyramid
Calculator for the number of stones in a two-dimensional and in a three-dimensional step pyramid. It is started on top with one stone, in the level below are two stones per dimension, then three stones and so on. Enter the number of levels to get the total amount of stones.
The number of stones can be calculated with the sum function. At a number of levels n, the formula for 2D is simply Σi for i from 1 to n. This can be converted into the function (n²+n)/2. The formula for 3D is Σi² for i from 1 to n.
Example: a pyramid with three levels has 6 stones in two dimensionds and 14 stones in three dimensions. Such cuboid-shaped stones are called ashlars.
In two dimensions, this shape isn't actually called a pyramid, but this name clearly indicates what it means. A centrally staggered stack of equal rectangles, so that an upper row doesn't protrude above a lower row. The number of rectangles in each row is odd, decreasing by two as you go up, and is finished when only one block remains in the row.
Usually referred to as pyramids are shapes with smooth sides. However, the first Egyptian pyramid, that of Pharaoh Djoser from the 27th century BC, was a step pyramid. In this case, the sides of each step were beveled. Many pyramids of the Central American Maya, such as the Pyramid of Kukulcán in Chichén Itzá, are constructed in a similar way. In all of these pyramids, however, the overlap was of much more than just one ashlar. The above calculation is a strong simplification and idealization; a corresponding structure would either require very large ashlars or result in a very small step pyramid. But these cuboids can be viewed as virtual cuboids which are composed of several real ashlars.
German: Dimension | Vielfacher Inhalt | Verhältnis | Diagonalen | Flächeninhalt | Rauminhalt | Schneiden | Stapel | Gitter | Anordnung | Rand | Innen-Außen | Lagerung | Ausbreitung | Stufenpyramide