Showing posts with label Greek architecture. Show all posts
Showing posts with label Greek architecture. Show all posts
Sunday, February 20, 2011
Sunday, January 30, 2011
The monument of Lysicrates
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.
Friday, January 28, 2011
The Tower of the Winds
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.
Friday, January 21, 2011
The temple of Olympian Zeus
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.
Wednesday, January 12, 2011
PARTHENON
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 3π 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?
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.
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.
Metopes and triglyphs.
Wednesday, January 5, 2011
Gla
Measurements: June 2002
Photos: June 7, 2002
*See "The Homeric Hyle" for new color diagrams and corrections.
The hill
The Gla hill is situated about 2.0 km SE of the modern village Kastro at the NE shore of the lake Kephisis (later Kopais) in Boeotia. The lake was drained around 1900, so the hill rises 25-40 m above the plain. Its shape is like a key or a pear and is about 850 m (West to East) amd 570 m (north to South).
The "Mycenaean" fortification around the hill is about 2650 m long. The polygonal walls are 4π MC (5.70 m) thick and have been built with large stones (now broken). In some places there were towers so the thickness there is greater.
The name of this important prehistoric city is unknown. The archaeologist Noack thought that it was the Homeric Arne. However, according to Stephanos Byzantios, Arne was the prehistoric name of Chaeronia, a city on the west side of this lake, west of Orchomenos.
Homer (Iliad 2, 500) mentions the most important Boeotian cities but none of them -except Hyle (Ύλη) fits in the NE end of the lake Kephisis. In Iliad (5, 708) he informs us that the hero Oresbios was living in the city Hyle next to the lake Kephisis. Although there is no proof, I believe that this acropolis is Hyle.
The first excavations on the hill were made by de Ridder (1894) and later by Threpsiades (1955-60) and Iacobides (1980-86). The large "Mycenaean" palace is built on the highest point and has two L-shaped wings with many rooms, corridors and sewers. The northern side is built over a precipice about 35 m above the plain.
The southern Gate
The walls of the Gate (ΑΔ and ΒΓ) are not exactly parallel, so the angle ΑΘΒ is not a right angle. AB is equal to the width of the lintel of the Treasury of Atreus in Mycenae.
There are two rooms for the guards on each side of the Gate. Both of them have the same width but the length of the one on the south side is twice its width.
General plan of the palace
The first part on the eastern side
The second part on the eastern side
The third part on the northern side
The north wall of this wing is built over a precipice about 35 m above the plain. There is a narrow path 1.5 m in width between the wall and the precipice, so it is easy to cross this side from H to K and Λ. The height of the wall above this path is 5-6 m. The NE corner at H is broken and most of the blocks have fallen down.
Although most thresholds are rectangular and their width is equal to the width of the walls, some of them have one of their sides rounded after the lines. The rounded part that is protruding is about 1 d lower than the rectangular part.
The fourth part
There are three thresholds between prodomos and domos without walls.
The perimeter of domos is 25π.
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).
Taken on May 18, 2002
The entrance of the Treasury of Minyas
Sunday, January 2, 2011
Tiryns
(See also "The acropolis of Tiryns" posted on 11 May 2012).
Tiryns is a very old city situated about 7 km East of Argos. It was founded in the precataclysmic period by the Pelasgian hero and king Tiryns, a descendant "son" of Argos, "son" of Zeus and Niobe. Later Proetus (or Proitos) became a king of Tiryns and put the Cyclops to build the cyclopean (megalithic) fortification around the acropolis. The hill is about 300 x 100 m.
The Megaron on the acropolis is rectangular and consists of three rooms: aethousa (hall), prodomos (meaning "before domos" and domos (the king's room). Outside the walls the length is 1599 d (25.93 m) and the width 773 d (12.535 m). Inside the length is 1504 d, but the width is 611 d in the north wall of the domos and 597 d in the beggining of aethousa. (* There is an important reason for all these inequalities in ancient architecture).
We observe that they have used many integral numbers in MC. The length of the domos is 26 MC (11.804 m) and is divided by the columns into three sections of 7, 12 and 7 MC. The doorposts are 2 MC and the openings 128 d (see the Treasury of Atreus, south wall). Also, the two diagonal lines meet at M (middle) at the beggining of domos.
Thursday, December 30, 2010
Mycenae
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)
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.
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