Showing posts with label cubit. Show all posts
Showing posts with label cubit. Show all posts

Tuesday, January 4, 2011

The Treasury of Minyas


Measurements: 18 May and 1 September 2002




Plan of the Treasury of Minyas.

Dromos. The walls of the dromos have been completely destroyed and it is impossible to measure its length and width.

Entrance. The width of the entrance on the threshold is 2.71 m (1.5 cm less than that of the Treasury of Atreus). Schliemann gives 2.71 m too. The arc is 1 cm greater, or 168 d (6 MC). This is three times the width of the threshold (3 x 56 d = 168 d).

Tholos. The length of each stone is given in d as it was measured in cm on the ground. I did not measure the bottom of the second row because it is about the same as the first one. At the corners B, B' of the entrance it seems that the curve of the tholos for the first three rows becomes greater instead of smaller. Then it turns towards the tholos and becomes gradually smaller. The circumference on the ground is about 2705 d, so the diameter is 861 d. According to Schliemann, the diameter is 13.84 m from South to North and 14.05 m from SW  to NE. The average is 13.945 m (or 860 d). I made three measurements of the diameter and found 866 d (14.045 m).



Detail of the corner of the entrance and the tholos.

Each block is different in size and the lines are not exactly parallel. The dashed lines show the points where other measurements were made for the height of two or three rows.

The length of the first block at B is 128 d (1 rod) in the entrance (top), or 3 times the height of the block (3:1).






The ceiling of the Burial Chamber





















Taken on May 18, 2002

The entrance of the Treasury of Minyas

Thursday, December 30, 2010

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.

Sunday, December 26, 2010

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.