Wednesday, December 29, 2010

The Treasury of Atreus (2)

4. The south wall of the entrance.

The south wall consists of 22 stones in nine rows, alternately two and three. The length AD on the ground is 320 d (5.189 m) or about 10(π-2) MC. The length of each row is given in the tholos.

The top of the third row is 12 MC as the height of the entrance.

The second stone of the second row is 4(π-2) MC, or 128 d (= 1 rod), equal to the height of the first three rows. It is also equal to twice the length of the first stone of the same (second) row.

The length of the lintel on the upper part (MM") is equal to the radius (Ro) of the tholos. They say that this gigantic lintel consists of two stones, but I think it is a monolith that has broken because of a strong earthquake. If we observe the lintel from the entrance, we will see that the "line" between the two  pieces is not perpendicular to the walls. I measured the distances from the beginning of the entrance and I found 1.69 m for the north wall and 1.91 m for the south. That's a difference of 22 cm! Ancient architects wound have never done this.

5. Plan of the entrance and the tholos

The length of the first row of stones in the entrance and around the tholos is given in d. Megalithic cubits (MC) are shown in bold numbers.

There are 28 stones in the tholos; seven of them are between the two entrances (at D" and Q) and 21 (3 x 7) between Q and D. The first three rings between the entrances consist of 7 stones.

The circumference of the tholos on the ground is the sum of the length of these stones plus 169 d for the first entrance and 92 d for the second. (The chord DD" is 168 but the arc is 169). Thus, the circumference is about 2831 d and the radius (Ro) 450.5 d, or 16.09 MC (7.305 m).

The first stone on the north wall is 115.5 x 77 (d), so the ratio is 3:2.

6. The curve of the tholos.

In this diagram I present the graph of the curve
y = ax^2 + bx , where
a = -1/50(π2) and β = 10/3π.

We observe that the points B, N, M, and S of the tholos are on, or very close, to this curve. Point B is at the end of the third row at the height of 128 d (see 4).

There are two vertical lines at A and K. The distance between them is the radius. KH is the height of the tholos (88/3 MC). We observe that HK = HB, HN = Hn, and HM = Hm.
(n and m are the points we get on the vertical line at A that correspond to the upper part of the lintel and the triangle).

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