Thursday, December 30, 2010


The acropolis of Mycenae is under the mountain on the white hill near the center of this picture.

The fortification of the acropolis near the Gate of the Lions (24 April 2002).

The Treasury of Atreus.

Detail of the entrance of the Treasury and the gigantic lintel.

The Gate of the Lions.

The Treasury of Atreus (3)

7. Lintel, tholos and burial chamber

The chords mm' and nn' are equal to the radius of the tholos (Ro = 450.5 d).

We observe that if we extend the lines of the lintel in the tholos, the circle KS (R17) is inscribed in them (diameter 2KS = FF').

ON = 91.31 d, but Dd is 93.27 d because it is the hypotenus of a small triangle (see 4).

8. The entrance of the burial chamber.

 In the case of this entrance, we obseve that the lintel consists of two stones and that the length of the second near the antichamber is 66 d. This means that the joint is perpendicular to the walls. Most Mycenaean lintels consist of two or three blocks that have been cut "straight" so that their joints are always perpendicular to the walls. However, the huge lintel of the main entrance consists only of one stone (monolith).

The length of the lintel on the eastern wall (bottom) is equal to the height of the four rows and the length of the fourth row on the western wall
(157 d = 50π). The length of this lintel on the eastern wall (top) is equal to the length on the western wall (bottom).

The Gate of the Lions

From Henry Schliemann's book
Mycenae - London 1878.

The Treasury of Atreus

From Schliemann's book.

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).

Tuesday, December 28, 2010

The Treasury of Atreus

First measurements: 24-26 April and 14 August 2002.
New measurements: 17 November 2007, 3 and 10 February 2008 and 2 March 2008.

1. Plan of the Treasury of Atreus.

There are 21 stones on the south wall of the dromos and 17 on the north (first row on the ground). Their length is given in d (ancient inches). The total length of the south wall is 2216 d and of the north wall 2206 d. So, the average in the middle (axis) is 2211 d, or 8π^2 MC (35.85 m).

The 15th stone on the north wall is huge and its length (387 d = 6.276 m) is about equal to the width of the dromos. This width is 390 d but in front of the entrance becomes 384 d (2 x 192 d). Now, 192 d is the height of the Gate of the Lions and its width inside (φ^4 MC). On the other side of  dromos (south wall) there are two other stones facing this one with a total length of 391 d.

2. The geometry of the facade projeted on the tholos.

OB is the radius of the tholos (450.5 d), equal to OF and OE.

The width of the entrance in the lintel is twice its thickness (height NM = 8/3 MC = 1.211 m)). The radius of the tholos (in this case OB) is equal to approximately 6 NM. The height of the tholos OH is 11 NM, or 88/3 MC (13.32 m). Some other important observations are given on the table on the left of this drawing.

3. Section of the Treasury

The north wall of the entrance consists of 23 large stones in nine rows. The length and the height of them is given in daktyloi (d). The total lenght of the north wall on the ground is 322.5 d (5.23 m) and the height (A' N) is 12 MC (5.45 m). The height of the tholos is 88/3 MC (13.32 m) and the upper part of the lintel (M) is in the middle (44/3 MC). The triangle above the lintel begins at E and the height
A" E is equal to the radius of the tholos on the ground (Ro = 16.09 MC = 7.306 m). The gigantic lintel occupies two rows of rings inside the tholos (10th and 11th). There are 33 rings and the lid on the top (at H) is the 34th (2 x 17). (The number 17 is very important).

Sunday, December 26, 2010

The Gate of the Lions

Measurements are given in Megalithic Cubits (MC, bold) and daktyloi (d).  1 MC = 28 d = 0.454 m.

1. The length of the threshold ΔΔ' is 12 MC (5.45 m), or twice the width of the Gate under the lintel (BB') and equal to the height of the entrance of the Treasury of Atreus. Some archaeologists write that it is 4.60 or 4.65 m, but they have measured up to the point where it is broken.

2. The width of the Gate at the threshold (AA') is MC (2.853 ) and in the lintel (BB') 6 MC (2.724 m). The height (ON) is 192 d, or φ^4,  ~ 6(π-2) MC (3.11 m).

3. The doorjambs in the front are π/2 MC, or 44 d in the middle, and 43 d near the threshold and the lintel.

4. The height of the lintel in the corners is π/2 (44 d) and in the middle 5/2 MC (70 d). So the total height of the Gate to the top of the lintel (OH) is 262 d (or 100φ^2). The length EE' is π^2 MC (4.481 m).

5. ΟΘ = ΘΣ = 227 d (3.681 m). Therefore, the height ΟΣ is 454 d or 16.21 MC (10φ MC).

Plan and section of the Gate of the Lions

The height of the Gate (192 d = 3.11 m) is equal to the width inside.

The pyramid near Argos

Photos taken on 12 July 1998 (User: Athang1504 in Google Earth, Panoramio, Flickr)
Measurements made on 3 May 2002
For the Megalithic Cubit (MC), see my first post.

Some well-known archaeologists believe that this small pyramid at Hellenikon (about 8 km SW of Argos, Peloponnesus) is not really a pyramid but a building of the Hellenistic Period (around 200 BC). However, Pausanias (B' 25,6) mentions a pyramid near Argos, built at the time of Acrisius and Proetus, kings of Argos and Tiryns, respectively. These twin brothers were ancestors of Perseus, ancestor of Heracles. Therefore, the pyramid is very old and was built by the Pelasgians.

This diagram presents the ground plan of the pyramid at the base and shows that the unit of length that was used is the Megalithic Cubit.

Saturday, December 25, 2010

The Megalithic Cubit

Copyright 2002 by Athanasios G. Angelopoulos
Published in 2003 in the book METRON ARISTON
ISBN 9608286069

In April 2002, I made the first precise measurements in the Treasury of Atreus and the Gate of the Lions in Mycenae, because I was interested in the unit of length that was used by the prehistoric architects. Some ancient Greek units of length that were given by archaeologists were not accurate (or even wrong) and did not agree with the measurements that existed at that time. Also, these measurements were very few and in most cases wrong, except those of Anastasios Orlandos for the Parthenon. For example, some books and encyclopedias wrote that the ancient Greek units of length were a foot of 0.3083 m (16 daktyloi = inches of 0.0193 m), a cubit of 0.4624 m (24 daktyloi) etc. But if an inch was 0.0193 m, then the foot was 0.3088 m and the cubit 0.4632 m.

After the measurements of the first three days (24-27 April), I found that the unit of length used by the Mycenaean architects was a cubit of 0.454 m. I called this unit "the Mycenaean Cubit". However, when in the following days and months I measured some other important monuments (including Parthenon), I found that this unit had been used by the Pelasgians long time before the Mycenaeans. Therefore, I changed the name and called it "the Megalithic Cubit" (MC). The MC was also used in historical times by all initiated architects.

Definition: The Megalithic Cubit is defined as 1: 14,000,000 of the Earth's polar radius (or 1: 28,000,000 of the Earth's polar diameter. Since the radius is 6,356,775 m, the MC is equal to 0.454055 m. It is also subdivided into 28 daktyloi, inches) of 0,01622 m). Now, this number (0.454) is a lot different from the one mentioned above (0.4624). Also, the reason they chose 14 or 28 is because these numbers are related to the period of the Moon. For example, there were 14 circles above the entrance of the Treasury of Atreus (not 16 as some artists draw) and 28 stones in the first row around the tholos.

Obviously, this means that many thousands of years ago, the Pelasgians and Mycenaeans knew precisely the size of the Earth and had advanced knowledge of geometry and mathematics. The Greek word γεωμετρία (geometria > geometry) means exactly "measurement of the earth".

A few examples:

1. The width of the entrance of the Treasury of Atreus is 6 MC (2.724 m). I made about ten measurements along the entrance and the width was 2.725 +/- 0.005 m. The height is 12 MC, or twice the width.

2. The first stone on the south wall of the same entrance is 5 MC (2.27 m).

3. The width of the Gate of the Lions on the threshold (and that of the similar Gate in Tiryns) is MC (2.853 m). The width of the Gate of the Lions in the lintel is 6 MC - the same as the width of the entrance of the Treasury of Atreus.

4. The width of the doorposts in the front of this Gate is π/2 MC (0.713 ); the length of the lintel is π^2 MC (4.481 m).

5. The dimensions of the Pyramid of Akrisios and Proitos at Hellenikon, Argos, are 33 x 28 MC (14.984 x 12.714 m). The large square chamber inside the pyramid is 15 x 15 MC (6.81 x 6.81 m).

6. The dimensions of the Parthenon on the stylobates are 68 x 153 MC (30.876 x 69.47 m).

Ancient architects did not use only the number π, but also the numbers φ (golden number = 1.618034), the natural logarithm e (2.71828) and many square roots.