Grouping
The "saw (or Christmas tree) curve" that I mentioned last week was just one continuing line all from the top to the bottom, but today, I am going to try dividing it into several groups by characteristic. The method is simple. It is merely to mark off at each point where the height suddenly increases. However, if a certain point seems more appropriate to be included in another group, I would move the point there. For example, there is a big depression at around 20 meters level in the group 2, but I would move that depression part to the group 1.

By managing it like this, I can divide it into 13 groups as shown in the figure. Yet, as it seems that groups 4, 5, 6, 7, and 8 can be divided into even smaller groups, there still is a possibility that the number of groups will increase.

The result would show a similar tendency all from the bottom to the top. In other words, the first stone is tall but then the height of stone decreases suddenly and almost continuously. What on earth does this really signify?

I keep working on the grouping work. The figure below has the same substance as the one above, but in this one, each group is shown from the starting point. The horizontal axis indicates the height of each group, but as the slope of the Great Pyramid is at regular angle, I can also show a horizontal distance from the origin by dividing it by 1.273 (See the calculation shown in the end.) From the figure, I find the following ideas.

• Within a certain group, there is a tendency that as the level gets higher (that is on the right side in the figure), the height of the block decreases.
• I can divide them broadly into three groups; Low (group 1), Middle (group 2-8), and High (group 9-13). The height of the Low group is the greatest while its rate of decrease is also the highest. On the other hand, there is not a big decrease in the height of the blocks in the High group.

How was the Great Pyramid built?
I now would like to consider how the Great Pyramid was built. A method of ramp is most commonly introduced. It is a theory arguing that people have built a gentle ramp with stones and bricks and lifted the blocks by using rollers and sleds. However, this theory has brought the following questions.

• No literature has been found to show the use of ramp.
• No trace of ramp has been found either.
• It is impossible in terms of engineering (or practically) to build a ramp as high as 150 meters above the ground by using clay and bricks. To put it simply, with clay and bricks, the ramp would be broken down with their own weight.
• If it is a ramp 150 meters high, probably only a few meters wide, with steep slopes on both sides without even a handrail, would it be really possible for dozens or hundreds of people to pull up a stone weighing as much as several tons to the top? That is a simple doubt I have. I suppose that you all have an experience of going up to an observation platform of such buildings as the Tokyo Metropolitan Government Office and Landmark Tower. At that place, which is at a great height where cars on the ground appears as nothing but mere beans, and is extremely narrow and surrounded by steep slopes, do you think that it is possible for dozens or hundreds of people to work together to pull up a stone weighing as heavy as the weight of several automobiles?

• As I have already mentioned, the pyramid has been built separately by groups. So, also with this theory, an explanation is necessary on that point.

This is how the pyramid has been built: the structure of steps was built at first. After completing the construction of certain steps, they raised the remaining stones by means of machines formed of short wooden planks. This machine raised them from the ground to the top of the first step. On this there was another machine, which received the stone upon its arrival, and conveyed it to the second step, whence a third machine advanced it still higher. Either they had as many machines as there were steps in the pyramid, or possibly they had but a single machineÉ The upper portion of the pyramid was finished first, then the middle, and finally the part that was lowest and nearest the ground.

How was the Great Pyramid built then?
Unfortunately, I do not know. But here is how I think.

• The builders of the Great Pyramid could handle blocks weighing as much as 50-80 tons. According to W. T Wallington, that is possible. Yet, whether his method was used or not is another question.
• As Herodotus has argued, the Great Pyramid was built by using a crane or similar machine. Each group shown above was covered respectively by a large craneÉI believe. However, such information as the crane's function is unknown.
• It is important to make a further investigation into the following issues.
1. What kinds of stones are piled up? And in what form?
2. How are the external stones related to the internal stones and structure?
3. Is it possible to apply the Wallington's method or other similar technique to the construction of the Great Pyramid in practice?

Translated by Maiko Noda