Sunday, January 30, 2011

The monument of Lysicrates

Measurements and Photographs: 3 October 2002.
The measurements were made only in the lower part of the monument.

The monument of Lysicrates is situated on Lysicrates Square in Plaka under the eastern side of the Acropolis. It was built by Lysicrates, the son of Lysitheides, around 330 BC.

This elegant, circular building consists of four steps made of conglomerate stone and a square base with four rows of blocks. On this base stands a circular monument, made of Pentelic marble, that has six semi-columns with Corinthian capitals. Their height is 3.55 m. Above the columns is the entablature with a circular epistylion (architrave) and a frieze depicting the myth of the transformation of the pirates into dolphins by Dionysos. On the top is the roof decorated with a large flower.

The eastern side of the monument of Lysicrates

Saturday, January 29, 2011

Hill of the Muses

Measurements: July - September 2002

The Hill of the Muses (Mouseion)

The Hill of the Muses, or Mouseion (200φ MC, 147 m above sea level), is located SW of the Acropolis, to the south of the Hill of the Pnyx. The hill was dedicated to the Muses but there was also a tradition that Mousaios, a friend and student of Orpheus, lived and died there.

Photo taken on September 14, 2002

As we approach the hill from the Acropolis, we find Socrates' prison in the foothills carved in the bedrock. It is about 80 m south of the Byzantine church of Haghios Demetrios.

Dipylon above the Gates (south side)

In front of the church is an ancient gate called "Dipylon above the Gates" and the "diateichisma" (inter-wall) that crosses the Pnyx (behind) and ends at the top of the Hill of the Muses (left). Part of the diateihisma can be seen behind these stones.

Kimon's tomb

About 70 m beyond the church and the gate (west) is Kimon's tomb (on the left) carved in the bedrock.


Beyond Kimon's tomb is the ancient deme (municipality) of Koele (or Koili) between the two hills.

Diateihisma (looking NW)

Near the gate there is an ascending path along the diateichisma that leads to the summit of the hill. This photo shows the part about 100 m before the top. The wall was built by the Athenians at the end of the 4th century BC and had square and circular towers. One of these is to the left of the picture.

 Mousaios' monument

The monument of Philopappos on the summit of the Hill of the Muses.

Friday, January 28, 2011

The Tower of the Winds

Measurements: 6 and 7 October 2002

The Horologion of Andronikos

The Horologion of Andronikos (Tower of the Winds) is an octagonal building made of white marble. It was built by the astronomer Andronikos from the city Kyrrhos of Macedonia around 100 BC and is situated in Plaka at the eastern end of the Roman Agora. Inside there was a cistern that was used as a clepsydra (water clock). The water was coming from the northern slope of the Acropolis through a pipe. On the outside it was decorated with a frieze of eight men in relief, representing the winds that blow from every direction, and a rotating bronze Triton on the top that showed this direction. The men were carved from left to right.

Wednesday, January 26, 2011

The Pnyx

Measurements: May - September 2002

The Hill of the Pnyx

The rocky hill is located to the west of the Acropolis between the Hill of the Muses and the Hill of the Nymphs. It was named Pnyx - from the word "πυκνός" (pyknos, dense) - because it was overpopulated.

The radius of the Pnyx, from the bema to the polygonal walls, is about the length of the Parthenon.

In historical times Pnyx was the meeting place of the Athenian ekklesia (assebly). The bema (step) was the
speakers' platform.

The length of the first step on the eastern side (facing the Parthenon) is 14 MC (1/100 of the radius-distance between Parthenon and this bema).

Friday, January 21, 2011

Ancient Athens

Measurements: July - September 2002
Photographs: 2010

A miniature of Gaia

These circles have all a radius of 1400 MC (635.6775 m). The first one around the Acropolis (K1) shows that some of the most important monuments of ancient Athens have been built about 1400 MC away from the center of the Parthenon.

If we stand on the summit of the Hill of the Muses (Monument of Philopappos), we'll see that the temple of Hephaestos and the summit of Mt. Parnes are in a straight line. If we walk a few steps away from this monument (at point E), we will observe that the center of the Parthenon and the summit of Lykabettos Hill are also in a straight line. The distance EL is 4r (two diameters).

The  Acharnikae or Acharnian Gates are located at the junction  of Aeolos and Euripides Streets under the National Bank of Greece (in the Themistoclean wall, north of the Acropolis).

Kotzia Square (looking SW)

The Acharnian Gates are near the upper left corner of this picture. This ancient road led to the deme (district) of Acharnae near Mt. Parnes.

Equal distances and alignments

In Kyllou Pera on Hymettos, Kephalos (or Cephalus), "son" (descendant) of Deion, "son" of Aeolos, killed his wife Prokris accidentally while they had gone there for hunting. This happened in prehistoric times before Herakles.

In this area there were many sanctuaries for Rhea, Demeter and Kore (Persephone), Aphrodite and Artemis, as well as a spring. The spring was called Kyllou Pera (or Kallia or Kylia) and its water was thought to be useful for the pregnant women. The Kaisariani Monastery was built on the same site with stones from the ancient ruins. The spring, to the east of the monastery, still exists today.

Prehistoric and ancient Greek architects, who were initiated in the Great Eleusinian Mysteries, did not build their temples, sanctuaries and other important monuments by chance; they were selecting the sites very carefully according to the oracles from Delphi and then used geometry. Everything had to be perfect. (Most other well-known people (philoshophers and writers) were not initiated in the Mysteries and they didn't know the great secrets).

The temple of Olympian Zeus

Measurements and photographs taken on 26 September 2002.

In prehistoric times the area around the temple (Olympieion) was sacred and dedicated to Zeus and other deities. There was a sanctuary of Olympian Gaia (mother Earth), a temple of Kronos and Rhea, and an old sanctuary of Zeus. It is situated 1400 MC (636 m) SW of the center of the Parthenon near the banks of the river Ilissos. The enclosure, built with poros stones, is 206 x 129 meters. According to Pausanias (A' 18), there was an old tradition that after the Cataclysm (* 9600 BC) the waters from the flood had disappeared there in a gap about a cubit wide. Then Deucalion built the old sanctuary for Zeus.

In historical times, the tyrant of Athens Peisistratos built a new temple between 560 and 540 BC. Later, when he died, his sons Hippias and Hipparchos, demolished it and started the construction of a colossal temple around 520 BC. However, the project was abandoned a few years leter when the tyranny was overthrown by the Athenians in 510 BC. In 174 BC, the Seleucid king of Syria Antiochos IV the Epiphanes - who thought that he was Zeus - continued the work with new designs by the Roman architect Cosssutius. Again, the construction stopped in 164 BC after Antiochos death. Finally the temple was completed by the Roman emperor Hadrian in 132 AD. Inside the temple (in Sekos) there was a colossal, chryselephantine statue of Zeus and a statue of Hadrian.

 Detail of the SE corner of the temple.

Monday, January 17, 2011


This work is based on the precise measurements given by Alexander Thom in his paper "Stonehenge" published by the Journal for the History of Astronomy (1974). Thom has also measured other megalithic sites in England and has found a unit of length called "rod"  equal to 2.5 megalithic yards (my) and approximately 6.803 ft.

According to Thom. the main circle of Stonehenge, the sarsen ring, consists of 30 large, upright stones. The inner faces of these stones is flat and polished and their width near the ground is 1 rod. The spaces between them are 1/2 rod, so the inner circcumference is 45 rods (30 x 1.5). The outer faces are rough and most of them rugged, but the mean thickness is 0.48 rods and the circumference 48 rods. These stones were capped by a complete ring of lintels that were cut to the curve of the circle and were all at the same level. Inside this sarsen circle there are three other rings of stones, the Bluestones and the Trilithons. On the outside, there are the Z, the Y and the Aubrey holes. Beyond the Aubrey holes is a ditch that surrounds the monument.

Thom writes that the Z and Y holes are not perfect circles but spirals with radii about 9 to 9.5 rods and 12.5 to 13 rods, respectively. The Aubrey holes have a radius of 141.80 ft and a circumference of 891.0 ft, almost precisely 131 rods. He adds that "if we assume that the intension was to make the circumference exactly 131 rods then we obtain a value for the rod of 6.802 ft which can be compared with the value found in Carnac of 6.803 ft at Le Menec and 6.808 at Kermario". On this circle there are "two so-called stations each of which consisted of a stone in the middle of a mound, the whole being surrounded by a ditch. The rectangle is completed by two station stones; both are still to be seen, one upright and one almost prostrate. There are idications in the underlying chalk that two other stones existed between the Aubrey circle and the bank".

It is obvious that the precise value of the "rod" is not well-known but it is approximately 6.803 ft. If the Aubrey holes have a mean radius of 141.80 ft, the circumference is 890.9557 ft (not 891.0). This means that if it was equal to 131 rods, the rod is equal to 6.8012 ft (not 6.802).

The sarsen ring
If the circumference of this circle is equal to 45 rods, the rod is 8 degrees, the spaces 4 degrees and the radius 45/2π rods. And if the value of the rod - according to Thom - is about 6.803 ft (2.07355 m), then 1 degree is about 0.2591943 m. But (π/2)-1 MC =
0.259173129 m! Thus,

1 rod = 4(π-2) MC = 2.073385 m
                               = 6.80244 ft

We also observe that the arc between the centers of two stones is 1.5 rods, or 6(π-2) ΜC = 3.110077 m
(φ^4 ΜC = 3.11216 m).

I have already mentioned that:

1. The height and the inside width of the Gate of the Lions in Mycenae is 6(π-2) MC (192 d or 3.11 m).
2. The second stone of the second row in the entrance of the Treasury of Atreus (south wall) is 4(π-4) MC (128 d = 1 rod). Also, the height of the first three rows on the same wall is 1 rod.
3. The length of this entrance (south wall) is 10(π-2) MC (319.646 d or 2.5 rods).
4. The width of the four doors in the palace of Tiryns is 4(π-2) MC (1 rod).
5. The diameter of the altar in front of this palace is 4(π-2) MC (1 rod).

The geometry of Stonehenge

(Using a ruler and a pair of compasses only).

Suppose that we draw a circle of radius 1. We inscribe this circle in the square ABCD and we bring the diagonals and the perpendicular lines in the middle. Using the four corners we write quarter circles of radius 2. Thus, we get the rectangle abcd and the points m, s, t and f. This is the basic geometry.

The rectangle abcd is about the same as the one in Stonehenge (formed by the "stations" in the Aubrey holes) and the stylobates of the Parthenon. We observe that the Y holes are inscribed in the quarter circles and the Z holes in the square formed by m, t, and their perpendicular lines on ab. Thus, if the radius of the Aubrey holes KB is 141.80 ft = 20.8437 rods, the radius Km of the Y holes is 12.21 rods and the radius of the Z holes is 8.63 rods. (The difference that exists is small).

Wednesday, January 12, 2011


Measurements: 11-15 October 2002

The architecture of the Parthenon

The "Old Parthenon" on the Acropolis of Athens, made of poros stone, had been destroyed by the Persians in 480 BC. Thirty three years later, in 447 BC, Pericles ordered the construction of the new Parthenon, a Doric order, peripteral temple made of white Pentelic marble. The architects were Iktinos and Kallikrates and the sculptor, who supervised the work and the decoration, was Pheidias. Pheidias himself made the chryselephantine (gold and ivory) statue of Athena Parthenos that was standing on a pedestal inside the temple. Her head reached the roof of the sekos (cella) which was 12.45 m high.

In this photo, taken on October 12, 2002, we see that the "new" Parthenon was built almost exactly on the pedestal of the "Old Parthenon". The difference is about 1 m to the north. (This is the south side - looking east).

The pedestal consists of a small base and three steps. The third step, where the outer columns of the peristyle stand, is called stylobates. There are 8 fluted columns in the narrow sides and 17 in the long sides. Thus, the total number of columns around the temple is 46, or 2(6+17) = 2 x 23. (*The number 23 is the arithmetic value of the Greek words "Η ΘΕΑ" (the goddess) if we add the numbers that correspond to each letter - e.g. Η=8, Θ=9, Ε=5, Α=1). In general, if the number of the columns on the narrow sides of an ancient Greek temple is α, then the number of the columns on the long sides is 2α+1 (twice the first number plus one).

Each column consists of 10 spondyloi (round pieces of marble put one on top of the other) and a capital (11 pieces). The total height of the columns above the stylobates is 23 MC (10.4433 m - 23 = Η ΘΕΑ). Above the capitals are the epistylia (= on the columns) that connect the columns. Above these long stones are the metopes serarated by the triglyphs. There are 92 metopes around the Parthenon, 14 in the narrow sides and 32 along the long sides. Now, the arithmetic value of the name ΑΘΗΝΑ (Athena) is 69 (Α=1 + Θ=9 + Η=8 + Ν=50 + Α=1).  Thus, the words Η ΘΕΑ ΑΘΗΝΑ (the goddess Athena) are equal to 23 + 69 = 92. Also, 69 is 3 times 23 and 92 is 4 times 23.

The height of the epistylia and the band with the metopes and triglyphs is 6 MC, and the height of the eaves and the pediment is 11 MC. Therfore, the total height of the Parthenon from stylobates is exactly 40 MC (23 + 6 + 11 = 40 MC = 18.162 m).

The entrances were on the east (main) and the west sides. After the first outer columns of the peristyle, there are two more steps and six smaller columns on the top of them and in front of the sekos (cella). The first part of the sekos on the east side - where the statue of Athena was standing - is called pronaos or prodomos and the second part on the west side opisthodomos (= back room). The total length of the sekos inside the walls is 44.166 m (29.7974 for pronaos + 13,2145 for opisthodomos + 1.154 for the wall between them). The width is 42 MC (19.065 m).

The dimensions of the sekos on its "stylobates" (including the walls and the 6 columns in the front and in the back) are 59.087 x 21.715 (m). The slabs of the frieze around the walls of the sekos were about 160 m in length and 1.05 m high. They were carved in situ and depicted the Panathenaic procesion.

The dimensions of the Parthenon

The width of the small base of the pedestal around the first step is 0.103 m and its height 0.30 m. The width of each of the next two steps is 0.70 m and their height 0.512 m. The height of the stylobates is 0.552 m.

The length of the base and steps on the four sides of the Parthenon is not exactly the same because the stylobates is not a perfect rectangular. The north side is 69.617 m, the south side is 69.5615 m, the east side is 30.9066 m and the west side is 30.963 m. The average is about 69.59 m for the long sides and 30.935 m for the short sides. In order to find the dimensions of the other steps and the base, we must add 1.40 m for each step and 0.206 m for the base.

The center of each column - with the exception of the four in the corners - has been put exactly on the joints of two adjacent blocks of the stylobates, so most of my measurements are between these joints (or the centers of the columns). For the four corner columns, I measured from the corners to the center of the next column. Because of the restoration work at that time, part of the north side was covered and I was not able to measure there. However, I took one measurement of the whole side.

For comparison, John Pennethorn (1878) writes that the dimensions of the Parthenon are 228.141 ft (69.537 m) and 101.336 ft (30.8872 m). According to Anastasios Orlandos (1949), the mean length is 69.556 m and the mean width 30.9205 m.

The mean distance between the centers of the columns - except for those in the corners - is MC (4.28 m). In the corners, the distance is 10π/3 MC (4.755 m). Thus, the length of the east side is 65π/3 or 68.068 MC (30.9066 m).

In ancient times, the Parthenon was called "ekatompedos neos" (100-foot temple) because the narrow sides on the stylobates were 100 ft. The long sides were 225 ft, so the ratio is 9:4. In 1984, I made the observation that if the mean circumference of the Earth is 40,030,375 m (360 degrees), then 1'' is equal to 30.8876 m. This was published in my first book "Omphalos" (Jan. 1986, p. 278). However, at that time I had not measured the Parthenon yet and I used the width we find in most books (about 30.88 m). But after my measurements in 2002, I found that this number was wrong and that the mean width is about 30.935 m. So, if we use the equatorial circumference of the Earth (40,075,161 m), 1'' is equal to 30.92 m. Is this a ...coincidence?

According to these numbers, the true dimensions in megalithic cubits are about 153,262 x 68.13 (MC). But the measurements were made along the curves of the stylobates - not in a straight line - so they are a little longer. The difference, of course, is negligible.

In the short sides, the difference of the curve  of the stylobates from the straight line between the corners AC is about 6.64 cm. In the long sides AB, the difference is 12.28 cm.

If the curves of the stylobates are arcs of circles, the radii KA are 68000/2π for the long sides and 400π^2 for the short. This means that the circumference of the first circle is 68000. But the number 68 is the width of the short sides.

 The geometry of the stylobates

We draw a circle of radius 84 MC. The number 84 is the arithmetic value for ΘΕΑ ΑΘΗΝΑ (goddess Athena). The diameter is 168 MC or approximately 17π^2 (167.8) and the circumference is 17π^3, or 527 MC.

First we inscribe this circle in a square of sides 168 and we bring the diagonals and the perpendicular lines in the middle. Each diagonal is about 238, or 14 x 17, so AK = 7 x 17 = 119. But ΠΑΡΘΕΝΩΝ / Η ΘΕΑ ΑΘΗΝΑ (Parthenon/the goddess Athena) is 1095 / 92 = 11.9.

If we use the corners A, B, C, and D and write circles with radii 168 and 84, we get the points a, b, c and d. The dimensions of the rectangle abcd is 153 x 68 MC and the ratio 9 : 4.



 Restoration of a broken capital on the floor of the sekos (October 2002).


Metopes and triglyphs.