Polar graphs

The great Mycenean tholos tombs

Excavations in the Treasury of Atreus
by Schliemann and his wife Sophia (1875).

From Henry Schliemann's book "Mycenae"
(London, 1878)

The great tholos tomb "Treasury of Atreus"

The tomb of Clytaemnestra

The tomb of Aegisthos

Tomb of the Lions

Tomb of the Lions - The lintel consists of three blocks

Tomb of the Lions - The upper part of the tholos has collapsed

Details in the entrance of the Treasury of Atreus

The southern base of the semi-column
(24 April 2002)

The passage (dromos) of the Treasury
and the large stone on the right.

The 15th stone (detail)

Another view.
It seems that the ground here was higher before.

The two semi-columns from 
the Treasury of Atreus 
National Archaeological Museum of Athens 

Detail of the decoration.
Only few pieces have been found.

The acropolis of Mycenae

First measurements and photos: April 2002
More measurements: 2007 and 2008

Coordinates:  37.7303   22.7578

The acropolis of Mycenae from the Treasury of Atreus.

The walls near the Gate of the Lions (center) and the acropolis (April 2002).

The tholos tomb of Clytaemnestra below Grave Circle A.

Grave Circle A.

The Megaron (Palace).

The underground cistern.

The Treasury of Atreus (more details)

*The first part was posted in December 2010.

The acropolis of Tiryns

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.

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).

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).