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 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.














10 comments:

  1. Hi Great Blog and You are a Great man.
    But...;) Ill find you because I organize 3D conference and I want to show virtual tour in Parthenon (Brand New).
    I use yours plans from 2002 because I want to build Parthenon stone by stone cm to cm and then convert to low poly. You can check curvature in WIP.
    But on the Google I can find only part of the plans do you do Measurements of the all parts of Parthenon or only some spots ? Contact me if you interested in participation ;) k.zwolinski.aka.blenderman@gmail.com

    The test and the WIP links :
    http://www.youtube.com/watch?v=QW5aR6rm1xg
    http://www.blender.pl/index.php?option=com_smf&Itemid=99999999&topic=9806.msg89019#msg89019

    ReplyDelete
  2. Thank you for your comment and interest. I have just posted some more measurements that cover the whole east side of Parthenon and the west entrance.I hope you'll find them useful in your work. Best wishes!

    ReplyDelete
  3. Hi great blog I really like the way you present this information regarding the monument itself and the design tectonics through reasoning and clear diagrams. After looking at your drawings I created some accurate details of the Parthenon in 3D with some parametric software.

    Have a look at http://www.shapeways.com/shops/architecturalobjects if you have time. There are images and you can order 3D printed models from this site too.

    I hope to build more detailed models including torus patch stylobate and column inclination in the future. Thanks for the cool blog.

    Regards

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  4. Thank you. I have seen your work and I think it is very good. I wish you good luck in the future with this project that you have in mind.
    Thanks again, and best wishes.

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  5. Can I just take a moment to THANK YOU SO MUCH for this blog! I'm crocheting a model of the parthenon for one of my classes and I've been trying to find accurate measurements EVERYWHERE - especially the stereobates. This has helped my project more than you can ever know!

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  6. Thanks for this blog, it's great! Do you know where I can get the book Metron Ariston? Have been looking for it in Australia and online, but can't find it anywhere! Any help would be great. Thanks again!

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  7. Penrose gives the column height (including capitol) as 31.423 feet (9.5777 meters). *

    The column height provided here is 10.4433 meters, a difference of 0.8656 meters.

    Do you know the source of the difference?

    It corresponds approximately to Penrose's capital height of 2.878 ft (0.8772 meters).

    Could this have something to do with it?

    *See East Front, Parthenon (Southern Half) in "The Principles of Athenian Architecture or The Results of a Recent Survey Conducted Chiefly with Reference to the Optical Refinements Exhibited in the Construction of the Ancient Building at Athens" (The Society of Dilettanti, London, 1851),

    Thank you,
    Christopher Arabadjis

    ReplyDelete
    Replies
    1. The height of the columns of the peristyle is measured from the stylobates (the top of the third step) to the epistylia (the long stones on top of the columns that connect them). This includes the capitals. I have already presented the diagrams including one for the capital (0.8685 m). Therefore, the total height of the columns is 23 MC or 10.4433 m.

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    2. Thank you for your reply. Your diagram is very clearly marked. May I ask if you made these measurements yourself? And if so were they done with a laser?

      My question above was why Penrose's results are different. I just found out that the second edition (1888) contains some corrections that include the measurement I was referring to.

      I was using the first edition (1851) available at the New York Public Library in NYC. The second edition (1888) is available online at the University of Heidelberg's website:
      http://digi.ub.uni-heidelberg.de/diglit/penrose1888

      Sincerely,
      Christopher Arabadjis

      Delete
  8. It is a shame that your book, Metron Ariston is not available as such on the internet (although your blog is a great source for some of it). You have done a lot of great work, by the look of it, and will help a lot in the pursuit of those of us who are interested in ancient metrology.

    Although, I have to admit that I believe that your idea of the square root of pi etc is, I think, a tad too complicated. I believe that maybe the numbers will fit better with John Michell and John Neal's work ... so that is what I am going to look at.

    Still a magnificent blog, and gives a lot of data on buildings and structures that it is extremely hard to find actual data on.

    Best wishes

    Harvey Price

    ReplyDelete