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1 Investigation

Published onApr 22, 2021
1 Investigation

The purpose of this study is to verify a theory concerning the ancient Greek system of site planning and to examine this system in relation to the culture as a whole rather than to check the precise details of its application at every site and at every period.

I investigated twenty-nine sites, two of which are Roman. The condition of these varies considerably, so that it is impossible to comment with equal assurance on all of them.* Only eight can be considered intact or authoritatively reconstructed: the Athens Acropolis III, the Asclepeion at Cos, the sequential layouts of the agora at Miletus, and the sanctuaries of Aphaia at Aegina, of Athena at Pergamon, of Zeus at Priene, of Demeter at Selinus, and of Poseidon at Sounion. These represent a very small proportion of the known sites, and certainly they do not suffice to demonstrate an irrefutable argument concerning the Greek system of planning. At some of the other twenty-one sites only parts of the layout could be observed and verified, so that my account of these is fragmentary. In short, the hypothesis presented here is based upon careful study of the few complete examples just mentioned and upon less thorough examination of a number of others. Imperfect evidence, I admit, makes it difficult to establish proof, yet in all the sites investigated—and they comprise the most important and best-preserved of those now known—I believe that I have traced the main outlines of a system of design. Even if future excavations show some of my conclusions to have been in error, I shall be content if I have succeeded in laying the foundation stone upon which others can later construct a valid and comprehensive theory. A preliminary hypothesis, whether it is right or wrong in detail, is essential to the process of scientific investigation: only after its initiation is there an incentive to test its accuracy.

The most important discovery resulting from this study, in my view, is that the Greeks employed a uniform system in the disposition of buildings in space that was based on principles of human cognition. The few variations in the system are related primarily to mathematical formulae, which are described later in this chapter. Although most of the sites described in this study are sacred precincts, I am convinced that the system prevailing there represents a general theory of spatial organization—a theory of city planning.

As far as we can judge from excavations, the temples of ancient Greece were better built and the sacred precincts more carefully laid out than other parts of the city: this is why their remains are more numerous than those of secular buildings. The relationship between a sacred precinct and a secular layout was the same as that between a temple and a secular building: the first was a more perfect exemplar than the second. Just as we can consider a temple as representative of Greek architecture, so we may consider the layout of an entire sacred precinct as typical of all Greek spatial complexes. The layout of the agoras at Miletus, Magnesia, and Pergamon, for example (see Figs. 32, 96, and 56), appears to have been governed by the same laws as that of the sacred precincts. Only one difference was found between the sacred precincts and the secular sites, and this may be circumstantial, as there are so few well-documented examples of the latter. The difference is in the angles of vision and the distances between the buildings: in the secular sites it was not possible to determine whether a specific angle of vision was used. The reason for this was, certainly in part, that the poor condition of some of the sites did not permit a precise determination of the position of all buildings. But we can perhaps assume that it was also because, as has just been mentioned, less exact proportions and measurements were used in these sites than in the sacred precincts.

Differentiation between sites that were planned and those that developed over a period of time may appear to present another difficulty. I believe, however, that this study demonstrates that all changes obeyed the same basic rules of architectural spacing. It is true that the rules were not followed exactly on every occasion, but on the whole they persisted—and here lies the interest for us today. It is not always easy to remember that these complexes were built by the ancient Greeks not as isolated objects, as we see them today, but as parts of a dynamic urban environment. As elements of a city they were subject to contemporary conditions of growth and change. They were not designed to satisfy the aesthetic demands of modern man for an ideal layout, an ideal city, unrelated to an actual time or place.

If we have hitherto failed to recognize that the urban layouts of the archaic, classic, and Hellenistic periods were organized on the basis of a precisely calculated system, it is because we are strongly influenced, consciously or unconsciously, by the rectangular system of coordinates (in which every point is established by its position on a plane in relation to two lines intersecting at right angles). This system was completely unknown to the ancient Greeks. Their layouts were not designed on a drawing board; each was developed on a site in an existing landscape, which was not subject to the laws of axial coordinates.

When a man stands in a landscape and looks about him, he sees its various features as part of a system of which he is the center and in which all the points on the plane are determined by their distance from him. If he wishes to establish the position of a tree, for instance, he notes that it is to his left at a distance of about 7 paces and that a second tree is somewhat further to his left at a distance of about 14 paces, or double the distance of the first tree. He does not automatically establish the position of the two trees in relation to abstract axial coordinates; he uses a natural system of coordinates. It was this system, known as the system of polar coordinates, that formed the basis of site planning in ancient Greece. The determining factor in the design was the human viewpoint. This point was established as the first and most important position from which the whole site could be observed: usually, it was the main entrance, which was often emphasized by a propylon. The following principles were used:

Radii from the vantage point determined the position of three comers of each important building, so that a three-quarter view of each was visible.

Generally, all important buildings could be seen in their entirety from the viewpoint, but if this was not possible, one building could be completely hidden by another; it was never partially concealed.

The radii that determined the comers of the important buildings formed certain specific angles from the viewpoint, equal in size on each site. These fell into two categories: angles of 30°, 60°, 90°, 120°, and 150°, corresponding to a division of the total field of 360° into twelve parts; and angles of 36°, 72°, 108°, and 144°, which resulted from division of the total field of vision into ten parts.

The position of the buildings was determined not only by the angle of vision but also by their distance from the viewpoint.

These distances were based on simple geometric ratios deriving from the angles of vision. Normally, the foot served as the basic unit of measurement, and the distances used were 100, 150, or 200 feet or those based on simple geometric proportions that could be determined on the site.

One angle, frequently in the center of the field of vision was left free of buildings and opened directly to the surrounding countryside. This represented the direction to be followed by the person approaching the site: it was the “sacred way.”

This open angle was usually oriented toward east or west or in a specific direction associated with the local cult or tradition.

The buildings were often disposed so as to incorporate or accentuate features of the existing landscape and thus create a unified composition.

The viewpoint from which these measurements were taken was crucial and was obviously situated not just anywhere within the main entrance, or propylon, but at a specific place within it. The examples studied show that this point lay where the mathematical axis of the propylon intersects the line of its innermost step (i.e., the final step before one entered the sanctuary) at a height of approximately 5′7″, the eye level of a man of average height.

Geometrical Relationships

A mathematical analysis of all the sites investigated is given in Tables 1–4, which show the development of the twelve- and ten-part system of architectural spacing. There is, on the whole, a conformity of mathematical relationships between certain angles of vision and certain distances between buildings. In some instances these relationships vary slightly. This does not necessarily imply that the system is faulty but rather that mathematical principles could not be precisely applied in every case. For example, some of the sites were developed over several centuries, and construction was carried out by different architects, who frequently had to change the original plans to meet new alterations or extensions. Sometimes the new composite plan could no longer follow the principles exactly because of new construction demands or because of a difficult terrain—factors that often upset calculations even today. Before pointing out inaccuracies in any given measurements, it is therefore necessary to take into account the far from ideal conditions under which most of the sites were constructed.

I believe that the physical limit of a structure (as seen from the vantage point) was measured from the edge of either the top step or the lowest step of the stylobate or from the edge of the cornice. All three measuring points were used, and this range of choice does not indicate a weakness in the system. In many cases the reason for the choice is apparent. For example, at the Athens Acropolis III (Fig. 5) the positions of the Erechtheion, the Parthenon, and the Chalkotheke were determined by their equidistance from point A. In the case of the Parthenon and the Erechtheion, this distance was measured to their lowest steps, because these are clearly visible from point A. But in the case of the Chalkotheke, the distance was measured to the top step (i.e., the base of the wall), as the lower steps are invisible from point A. The distance between the base of the wall of the Chalkotheke and the top step of the Parthenon is equal to the distance of each of these two buildings from point A.

It appears that one of the two following mathematical schemes was used (see Tables 1–4):

Twelve-Part System

The layout of the site was determined by angles of vision of 30°, 60°, etc., dividing the entire 360° into twelve equal parts. Distances between buildings were aa, a/2a/2, a/2aa/2a, or a3/2a\sqrt{3}/2; i.e., all were governed by a 60° angle. The area was thus divided into twelve equal parts.

Ten-Part System

The layout was determined by angles of vision of 18°, 36°, 72°, etc., dividing 360° into ten equal parts. In this case distances between buildings were a/ba/b, (a+b)/a(a +b)/a, (2a+b)/(a+b)(2a + b)/(a + b), etc; i.e., they followed the golden section, which is determined by the isosceles triangle with an angle of 36° = 180°/5. The entire area was thus divided into ten equal parts.

There is but one complete exception: the precinct of the Egyptian gods at Priene, in which sight angles of 45° and 90° (i.e., an eighth part of 360°) were consistently employed. The reason may be that this was a foreign, not a purely Greek, cult.

It appears that all sites in the same city, or the same locality, employed the same mathematical system, for example,

  • Athens: Acropolis II and Acropolis III used the equilateral triangle (see Figs. 4, 5).

  • Cos: All three terraces used an angle of 360° (180/5) and the golden section (see Fig. 77).

  • Pergamon: The sanctuary of Athena, the agora, and the altar terrace used angles of 30° or 60° (see Figs. 61, 56, 64).

  • Priene: The agora and the sacred precincts of Zeus and Demeter used an angle of 36° and, in part, the golden section (see Figs. 84, 93, 120).

  • Samos: The Heraion of Rhoikos and subsequent layouts used 36° and the golden section (see Fig. 70).

  • Sounion: The sacred precincts of Poseidon and Athena used angles of 30° and 60° (see Figs. 52, 117).

There seemed at first to be several possible explanations for the use of two variations of the system: differences between cults and between individual deities; differences between the Greek peoples and in relations between cities; differences in architectural styles. Careful examination of the sites, however, eliminated two of these possibilities: differences between the deities had to be discounted, as both systems were used for the same deity (e.g., the sanctuary of Athena in Pergamon was based on the twelve-part system, but the ten-part system was used for her sanctuary at Priene); differences between the Greek peoples also had to be dropped, as both systems were in use in Ionian cities. The only plausible explanation seemed to be that the system depended on the architectural style employed. In general, when the buildings in the sacred precinct were in the Doric style, the twelve-part system was used; when in the Ionic style, the ten-part system was used.

In the following nine sites (listed chronologically) the buildings were in the Doric style and the twelve-part system was used:

  • Delphi, terrace of Apollo, sixth century B.C. (see Fig. 8)

  • Athens, Acropolis II, fifth century B.C. (see Fig. 4)

  • Aegina, sacred precinct of Aphaia, fifth century B.C. (see Fig. 19)

  • Miletus, Delphineion I, fifth and fourth centuries B.C. (see Fig. 23)

  • Olympia, Altis, fifth century B.C.

  • Sounion, sacred precinct of Poseidon, fifth century B.C. (see Fig. 52)

  • Miletus, Delphineion II, third century B.C. (see Fig. 24)

  • Pergamon, agora, third century B.C. (see Fig. 56)

  • Pergamon, sacred precinct of Athena, second century B.C. (see Fig. 61).

The following two sites with buildings in the Doric style used the ten-part system:

  • Cos, Asclepeion, fourth century B.C.-second century A.D. (see Fig. 77)

  • Priene, sacred precinct of Demeter, fourth century B.C. (see Fig. 120)

The following five sites with buildings in the Ionic style used the ten-part system:

  • Samos, Heraion II, in the time of Rhoikos, mid-sixth century B.C. (see Fig. 70)

  • Samos, Heraion III, of the classical period, late sixth century B.C. (see Fig. 71)

  • Priene, agora, late fourth century B.C. (see Fig. 84)

  • Priene, sacred precinct of Zeus, third century B.C. (see Fig. 93)

  • Magnesia, sacred precinct of Artemis, second century B.C. (see Fig. 95)

Sounion, sacred precinct of Athena, fifth century B.C., with buildings in the Ionic style, used the twelve-part system (see Fig. 117).

Athens, Acropolis III, fifth century B.C., with buildings in the Doric and Ionic styles, used both the twelve-part and ten-part systems (see Fig. 5).

The exceptions may perhaps be explained as follows:

Cos: The temple of Asclepios was built in the Doric style, but the angle of 36° and the golden section were used to determine the positions of the buildings and the distances between them. This may be because the sacred precinct was built toward the end of the Hellenistic period, when the architectural orders had become intermingled. The Doric columns here have Ionic proportions, and, indeed, the whole site already shows signs of Roman influence.

Priene: The sacred precinct of Demeter was also built in the Doric style but followed the ten-part system. This is the only outstanding exception to the rule. It could be argued that it provides evidence that the two systems were related to differences between the peoples of ancient Greece, although this is not borne out in other cases. As I have said, scarcity of examples prevents complete substantiation of my theory, and each case must be considered individually.

Sounion: The sacred precinct of Athena seems also to be an exception in that the building is Ionic, but the layout appears to follow the twelve-part system. As the location of the entrance has not been precisely determined, however, this example cannot be considered definitely contrary to the rule.

Athens: At the Acropolis III of Athens the majority of the buildings are in the Doric style, but the Erechtheion is purely Ionic. In general the 30° angle and proportions of 1:2 were used, but in subdivisions, angles of 18° and 36° were used with the golden section. It thus appears that both mathematical systems were used at this site, which contains important buildings in both styles.

Priene: The sacred precinct of the Egyptian gods, as has already been mentioned, was a foreign cult, and this may account for the organization of the site on the basis of 45° and 90° angles.

Selinus: The sacred precinct of Demeter appears to be organized on the basis of the angle of 90°, but the site is not sufficiently well documented for this to be certain.

There was yet another major difference between the two types of layouts in their organization of architectural space. In the first group, in which the Doric style and the twelve-part system were used, a path always formed an important feature in the disposition of the buildings in relation to the landscape. Sometimes this path divided the layout into two separate complexes; sometimes it acted as an open axis, left unobstructed as far as possible, so that the eye could look out far into the distance. By contrast, the layouts of the second group, in which the Ionic style and the ten-part system were employed, had closed views or presented an impression of enclosure, and a path was wholly incorporated within the layout. At the Heraion II (Rhoikos period) in Samos this effect of a closed view is particularly noticeable. After the destruction of the Rhoikos temple by fire, a large square was created in front of the new temple, Heraion III, but at the same time this was bordered by a long line of monuments that effectively closed the view (Fig. 71). In both the twelve- and ten-part systems it can be discerned that an attempt was made, whenever possible, to bring the outlines of the buildings into harmony with the lines of the landscape.

The open axis in the twelve-part system was sometimes oriented toward the east and sometimes toward the west. We can assume that this was consciously done so that a person entering the site by the propylon and following the open path had a clear view of the sunrise or sunset. In the case of the Athens Acropolis, for example, this axial view was held open in all of the three different layouts of the site, probably to allow an uninterrupted view of the sunrise at the time of the Panathenaic Festival. A similar intention can be observed in the closed Ionic layouts. As one enters the propylon at Samos, for instance, one faces a relatively low altar above which the sun can be seen rising from behind Mount Mykale.

Table 1
Use of the Twelve- and Ten-Part System


Acropolis I

Acropolis II

Acropolis III


ca. 530 B.C.

ca. 480 B.C.

after 450 B.C.

Angles of vision

3 equal angles of ca. 16°

π6+π6+π6+π6+π6+π6\frac{\pi}{6} + \frac{\pi}{6} + \frac{\pi}{6} +\frac{\pi}{6} +\frac{\pi}{6} +\frac{\pi}{6}

π6+π6+π6+π6\frac{\pi}{6} +\frac{\pi}{6} +\frac{\pi}{6} +\frac{\pi}{6}

π10+(π6π10)+...\frac{\pi}{10} + (\frac{\pi}{6} -\frac{\pi}{10}) + . . .


x + 2 = 2y
y:2y =
arithmetic progression

x,x32x, \frac{x\sqrt{3}}{2}

x3,2x3,x,4x3,5x3\frac{x}{3},\frac{2x}{3}, x, \frac{4x}{3}, \frac{5x}{3}

x2,x,3x2\frac{x}{2}, x, \frac{3x}{2}
(golden section)



x3\frac{x}{3} = 30.8 m

= 100 pre-Periclean feet


Proportions of buildings

Hecatompedon 1:2
Parthenon I
1:(1+2)1:(1 + \sqrt{2})

Hecatompedon 1:2
Parthenon II
1:8:31: \sqrt{8}:3
Stoa 1:8:31: \sqrt{8} :3

Parthenon 1:
Chalkotheke 1:
Erechtheion 1:2:31:2:\sqrt{3}
Propylaea 1:31:\sqrt{3}

Basis of layout

Proportion 1:2
Clear view to east

Equilateral triangle
Clear view to east

Equilateral triangle and golden section
Clear view to east

General orientation of site




Table 2
Use of the Twelve-Part System


Terrace of Apollo

Sacred Precinct of Aphaia

Miletus, Delphineion I



530 B.C.

500–470 B.C.

479 B.C.

470–456 B.C.
4th cent. B.C.

Angles of vision

π3,π3,(π4)\frac{\pi}{3}, \frac{\pi}{3}, (\frac{\pi}{4})




π3+π6,π6+π12\frac{\pi}{3}+\frac{\pi}{6}, \frac{\pi}{6}+\frac{\pi}{12}










2x = 30.8 m
= 100 pre-
Periclean ft

x = 80 m
= approx. 250 Doric ft

Proportions of buildings


(lowest step)

Complete layout 2:3

Temple of Zeus 1:51: \sqrt{5}
Heraion ca. 1:8:31:\sqrt{8} :3
Metroon 1:2

Field of vision

Determined by the angle of 60°. Clear view to south.

Determined by equilateral triangle. Clear view to north.

Determined by equilateral triangle.

Determined by equilateral triangle.

General orientation of site





Sounion, Sacred Precinct of Poseidon

Miletus, Delphineion II

Pergamon, Agora

Pergamon, Sacred Precinct of Athena

Miletus, Delphineion III-IV

450 B.C.

334 B.C.

3rd or 2nd cent. B.C.

197-159 B.C.

Late Hellenistic to early Roman period













x = 52.40 m
= 100 ells



Temple of Poseidon 1:51:\sqrt{5}

Complete layout 1:31:\sqrt{3}

Agora temple 1:3:21:\sqrt{3}:2

Temple of Athena 1:3:21:\sqrt{3}:2


Determined by equilateral triangle.

Determined by equilateral triangle.

Determined by equilateral triangle.

Determined by equilateral triangle.

Determined by equilateral triangle.

Southward (Westward?)





Table 3
Use of the Ten-Part System


Samos, Heraion II

Samos, Heraion III

Priene, Agora

Cos, Asclepeion, Lower terrace


ca. 550 B.C.

End of 6th cent. B.C.

2nd half of 4th cent. B.C.

300-250 B.C.

Angles of vision






(golden section)

(golden section)




x + y = 69.80 m
= 200 Ionian ft

x + y = 69.80 m
= 200 Ionian ft



Proportions of buildings

Rhoikos temple 1:2

Heraion 1:2


Lower terrace 1:2

Field of vision

Determined by triangle with angles of π5\frac{\pi}{5}(36°)

Determined by triangle with angles of π5\frac{\pi}{5}(36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

General orientation of Site





Priene, Sacred Precinct of Zeus

Magnesia, Sacred Precinct of Artemis

Cos, Asclepeion, Upper terrace

Cos, Asclepeion, Middle terrace

Palmyra, Small temple precinct

3rd cent. B.C.

158 B.C.

ca. 160 B.C.

2nd cent. A.D. and earlier

1st cent. A.D.






(golden section)

(golden section)

(golden section)

(golden section)

(golden section)

x + y = 34.94 m

= 100 Ionian ft

x + y = 104.8 m

= 300 Ionian ft

x + y = 69.80 m

= 200 Ionian ft




Temple of Artemis 1:3:21:\sqrt{3}:2

Temple of Asclepios 1:2

Temple B 1:3:21:\sqrt{3}:2
Altar 1:21:\sqrt{2}

Temple 1:51:\sqrt{5}

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)

Determined by triangle with angles of π5\frac{\pi}{5} (36°)






Table 4
Use of Exceptions to the System


Selinus, Sanctuary of Demeter

Sounion, Sacred precinct of Athena

Priene, Sacred precinct of Demeter

Priene, Sanctuary of the Egyptian gods


6th cent. B.C.

480–450 B.C.

2nd half of 4th cent. B.C.

3rd cent. B.C.

Angles of vision















Proportions of buildings


Temple of Athena earlier 3:4:5
later 3:4:5


Altar 1:2

Field of vision



Determined by triangle with angles of π5\frac{\pi}{5} (36°)


General orientation of site





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