The Athena Temple at Paestum and Pythagorean Theory Nabers, Ned;Ford Wiltshire, Susan
Greek, Roman and Byzantine Studies; Fall 1980; 21, 3; Periodicals Archive Online pg. 207

The Athena Temple at Paestum 
and Pythagorean Theory 

Ned Nabers and Susan Ford Wiltshire 

T HE LACK of contemporary evidence for Pythagorean activity 
in southern Italy during Pythagoras' own time there, roughly 
53211 to 49413 B.C.,l causes us to examine with special in­

terest the case for Pythagorean qualities in the design of the temple 
of Athena at Paestum, which is commonly dated to around 510 
B.C. In a study published in 1958 H. Kayser attempted to demon­
strate that the number theories of Pythagorean philosophy influ­
enced the design of the temple. 2 Although the results of his study 
were questionable at best,3 the idea that this temple incorporated 
tenets of Pythagoreanism was taken up again by R. Ross Holloway 
in 1966.4 Basing his arguments on the precise measurements of the 
temple published by F. Krauss,s Holloway clearly demonstrated 
that the number four, the creative principle in Pythagorean thought, 
and the numbers ten and twenty-four permeate the fundamental 
design of the temple. We wish to offer here further evidence cor­
roborating this thesis. 

The crucial importance of the numbers four, ten, and twenty­
four to Pythagorean philosophy derives from the discovery by 
Pythagoras that intervals in the musical scale could be expressed 
by mathematical ratios involving the first four integers. 6 Here was 
empirical evidence, it was felt, for an inherent order in the uni-

I G. S. Kirk and J. E. Raven, The Presocratic Philosophers (Cambridge 1957) 217ff, 
review the biographical evidence, most of which is late and obscure. The tradition was that 
Pythagoras left his native Samos and settled in Croton in 532/1. E. L. Minar, Jr., Early 
Pythagorean Politics (Baltimore 1942) 133-35, suggests 494/3 for his death. 

2 Paestum: Die Nomoi der drei altgriechischen Tempel zu Paestum (Heidelberg 1959) 
49-60. 

3 See R. Ross Holloway, "Architettura sacra e matematica pitagorica a Paestum," Par Pass 
106 (1966) 64 n.lO. 

4 Holloway (supra n.3) 60-64; cf. his A View of Greek Art (Providence 1973) 64-68. 
5 Die Tempel von Paestum 1.1 (Berlin 1959). 
6 W. K. C. Guthrie, A History of Greek Philosophy I (Cambridge 1962) 220-22, dis­

cusses the attribution of the discovery to Pythagoras and generally accepts its authenticity. 
The ratios are 1:2 (octave), 3:2 (fifth), and 4:3 (fourth) (Guthrie 223). 

207 



208 THE ATHENA TEMPLE AT PAESTUM 

verse. 7 Ten, as the sum of the first four integers, was considered by 
the Pythagoreans to be the perfect (reA..c:lOv) number, comprising, 
in Aristotle's terms, the whole nature of numbers (mzaav •.• r1]v 
rwv apz(}/1wv cpvazv, Metaph. 986a8-9). The four integers were 
represented graphically as an equilateral triangle with one point at 
the top, followed by two points and three more under them, then 
four at the bottom. This figure, called the rc:rpal<TVC;, was a sacred 
emblem for the Pythagoreans, who were said to swear by their 
leader in the following formula: "by him who handed down to us 
the tetractys, source and root of everlasting nature."8 Further, as 
the sum of the four numbers of the tetractys is ten, so their product 
is twenty-four. 

We begin with the matter of the length of the stylobate of the 
Athena temple, determined by Krauss to be 100 Doric feet (each 
measuring 0.328 m.).9 This of course is not remarkable, because 
many Greek temples incorporated the measurement of 100 units 
in their plans. 10 It does raise the problem, however, of the length 
of the foot used in the construction of the Athena temple, espe­
cially since W. B. Dinsmoor has asserted that an Ionic foot of ca 
0.294 m. was employed at Paestum. ll 

7 Pythagoras is said to have been the first to attach the term /(0<1110C; to the natural world, 
thus affirming the orderliness and arrangement perceptible within it; see Kirk and Raven 
(supra n.l) 229 n.3 for an assessment of the evidence. The implications of this discovery 
were for the Pythagoreans ethical and religious as well as scientific-by studying and 
conforming ourselves to the orderly structure of the universe, we ourselves can become 
/(0<111'01; cr. W. K. C. Guthrie, The Greek Philosophers (London 1950) 37-38. 

8 Porph. Vit.Pyth. 20, ov, Wi rov al1ereW yeve(i napaJovra rerpa/(ruv, nayciv devdov 
rpumoc; pI(wl1ar' lxov<1av; cr. Iamb\. Vit.Pyth. 150. 

9 Krauss (supra n.5) 2. C(. J. J. Coulton, "Towards Understanding Doric Design: the 
Stylobate and Intercolumniations," BSA 69 (1974) 81. 

10 Cf. Holloway (supra n.3) 63. One might also point as an example of this practice to 
the other great sixth-century temple at Paestum, the first temple of Hera, which stands a 
few hundred meters to the south of the At"ena temple. According to Gruben in H. Berve, 
G. Gruben, and M. Hirmer (Greek Temples, Theatres, and Shrines [New York 1962]409), 
that temple measures 100 Ionian ells or cubits (= 1112 feet) from the axis of one corner 
column to the axis of the other corner column along its longer sides. This would show that 
the practice of calculating distances in temples from the axis of one comer column to the 
axis of another corner column was established at Paestum long before the erection of the 
temple of Athena. 

11 "The Basis of Greek Temple Design: Asia Minor, Greece, Italy," Atti del Settimo 
Congresso Internazionale di Archeologia Classica (Rome 1961) 358. If this is so, the 
principle of 100 units would be negated in the length of the earlier Hera temple (supra 
n.10) as measured from one corner column axis to another. In order for that idea to be 
valid a foot of ca 0.351 m. would have to have been used, which corresponds to Dinsmoor's 
(360) Samian, Ptolemaic, or Philetaeric foot of ca 0.350 m. 



NED NABERS AND SUSAN FORD WILTSHIRE 209 

Dinsmoor did not give his evidence for such a foot at Paestum 
but did state that among nine examples of such an Ionic foot in 
southern Italy averaging 0.29395 m., four came from Paestum 
and Foce del Sele. He gave some of the dimensions of the three 
major temples at Paestum in terms of feet ca 0.294 m., including 
two from the temple of Athena: the diameter of the columns (45/16 
Ionic feet) and the height of the columns (20% Ionic feet).12 But 
Dinsmoor's case for such an Ionic foot in the temple of Athena is 
not argued. His thesis that in the Greek world there were only two 
widely used feet-an Ionic foot of ca 0.294 m. and a Doric foot of 
ca 0.3265 m. 13-does not seem to have won wide acceptance. It 
is prudent here to recall Broneer's statement that "it is essential ... 
to bear in mind that in a Doric temple the one basic dimension 
with immediate bearing on the foot measute is the length of the 
stylobate."14 In the Athena temple the stylobate is 32.883 m. long, 
or 0.083 m. longer than precisely one hundred feet of 0.328 m. 
The error amounts to one-quarter of one percent and may be com­
pared with the error of up to 0.15% which Dinsmoor found in 
mechanically manufactured wooden meter sticks sold in modern 
Athens. 1s 

Krauss has demonstrated, furthermore, that a Doric foot of 
0.328 m. fits so nicely into some of the other measurements of the 
building that the burden of proof, we believe, now rests on anyone 
who would deny that this was the unit of measurement used: the 
height of the columns of the peristyle is 6.122 m. (or 18 213 Doric 
feet), the height of the entablature from the top of the abacus to 
the top of the sima is one-half the column height of 3.062 m. (or 
9% feet). The width of the triglyph is 0.550 m. (or 12/3 feet), the 
width of a normal metope is 0.7625 m. (or 2% feet), while the 
width of the corner metopes is 0.9855 m. (or 3 feet). In the Ionic 
porch in front of the cella the columns have an interaxial of half 
that of the Doric columns of the peristyle (2.626 -:- 2 = 1.313 m. 
or 4 feet); their lower diameter is 0.820 m. (or 2% feet) and their 
upper diameter is 0.656 m. (or 2 feet). The height of the architrave 
is 0.574 m. (or 1 % feet).16 Furthermore, as Holloway has ob-

12 Dinsmoor (supra n.ll) 367. 
13 Dinsmoor (supra n.ll) 355 -60. 
14 Oscar Broneer, Isthmia I: The Temple of Poseidon (Princeton 1971) 177. 
15 Dinsmoor (supra n.11) 357. For a different view of the stylobate of this temple see 

Malcolm Bell, "Stylobate and Roof in the Olympieion at Akragas," AJA 84 (1980) 364. 
16 Krauss (supra n.5) 2, 3, 5, 17, and Abb. 43. 



210 THE ATHENA TEMPLE AT PAESTUM 

served, a foot of 0.328 m. is hardly extraordinary in the Greek 
world. 17 

The Athena temple has a peculiar characteristic which it shares 
with only one other Doric temple: all of the interaxials of the peri­
style are uniform, on the fronts as well as on the flanks, with no 
corner contraction for the solution of the Doric angle conflict.18 

While it is certainly normal for a sixth-century Doric temple in 
southern Italy or Sicily to have no corner contraction, it remains 
that the Athena temple at Paestum is unique in the archaic period 
in having uniform interaxials all around the peristyle. And al­
though at the end of the sixth century B.C. it was becoming com­
mon practice to have the front and flank interaxials the same, the 
Athena temple was possibly the earliest example of this practice 
and is certainly the only Doric temple at this time to combine uni­
form interaxials with the lack of corner contraction. The only 
other Doric temple to display this same uniformity of interaxials is 
the peripteral temple of Apollo on Delos which was begun in the 
fifth century B.C. In the case of the Apollo temple there is clear 
explanation for its uniform interaxials: the temple was begun in 
the Ionic order. Work on it seems to have stopped in 454 B.C. 

when the treasury of the Delian League was transferred to Athens; 
when the work was resumed ca 315, the design of the peristyle 
was changed to Doric. Since the lower steps of the krepis had al­
ready been laid, however, the joints of the stylobate and the place­
ment of the columns of the peristyle followed the uniform spacing 
of the joints in the lower steps of the krepis which had anticipated 
an Ionic peristyle. 19 

Holloway's contribution is to show that the peristyle of the 

17 Holloway (supra n.3) 62 n.7. 
18 It should be noted here that the interaxials vary slightly but were all obviously in­

tended to be the same. Krauss (supra n.5) 3 (cf. 17) states: "Die Saulenjoche sind ringsum 
gleich und betragen im Mittel 2,626 m. Die Saulen stehen senkrecht, der Tempel hat keine 
Kurvatur." The difference between the widest and the narrowest interaxial is only 0.072 m. 
(Krauss, Tafel 11). These very small variations between one interaxial and another are quite 
normal in a limestone temple such as this and occur even in classical marble temples like the 
Parthenon (cf. A. W. Lawrence, Greek Architecture [Baltimore 1957] 173 fig. 98). The 
average interaxial of the Athena temple, as determined by Krauss, is 0.002 m. longer than 
precisely 8 Doric feet of 0.328 m. E. Lorenzen's tables (Along the Line Where Columns Are 
Set [Copenhagen 1970] 147) show a difference of 0.004 m. between the interaxials on the 
fronts and those on the fa~ades, but this is not supported by Krauss' careful measurements 
or by the figures in W. B. Dinsmoor's list (The Architecture of Ancient Greece [New York 
1950] following p.340). 

19 Dinsmoor (supra n.18) 184 and 221. 



NED NABERS AND SUSAN FORD WILTSHIRE 211 

Athena temple at Paestum is based on a module of four Doric feet, 
each interaxial being uniformly eight Doric feet (2.626 m.) or 
twice the basic module, and that the rectangle of the peristyle, 
measuring from the axes of the corner columns, is 40 (or 4 X 10) 
Doric feet by 96 (or 4 X 24) Doric feet. 20 With his analysis Hollo­
way has demonstrated persuasively the Pythagorean basis of the 
temple design. 

The importance of the numbers four, ten, and twenty-four to the 
fundamental plan of the temple, however, goes even further. On 
the plan of the temple, and again measuring from column axis to 
column axis, a triangle formed from any two adjacent sides of the 
peristyle and a line extending from one corner column to its diag­
onal opposite (Figure 1)21 will demonstrate Pythagorean qualities. 
One side of the triangle measures 40 (or 4 X 10) Doric feet, an­
other side 96 (or 4 X 24), while the hypotenuse will be the square 
root of 402 + 962 = 1600 + 9216 = 10,816, or 104 Doric feet or 
10 X 10 + 4-each factor a Pythagorean number. 

Figure I: PLAN R. A. Baldwin 

Another way of looking at such a triangle is to observe that 
while one side measures 4 X 10 Doric feet, the other two sides 
measure 102 - 4 and 102 + 4 respectively. It is important to re­
member that while for every right triangle the square of the hy­
potenuse will equal the sum of the squares of the other two sides, 
only an occasional right triangle will have the length of all three 

20 Holloway (supra n.3) 63. 
21 We gratefully acknowledge that an undergraduate at Vanderbilt Universiry, Mr Joel 

Upchurch, first pointed out the existence of such a triangle in the plan of the temple and 
that the length of its hypotenuse was 104 Doric feet. 



212 THE ATHENA TEMPLE AT PAESTUM 

sides expressed in whole numbers. Such a right triangle is termed a 
'perfect' or 'pythagorean' triangle in mathematics, and there are 
only sixteen basic pythagorean triangles with an hypotenuse less 
than one hundred. 22 The pythagorean triangle present in the plan 
of the Athena temple at Paestum is a version of the basic or primi­
tive pythagorean triangle 5, 12, 13, enlarged by a factor of 8. 
Furthermore, as 40 + 96 + 104 equal 240, the perimeter of this 
triangle measures 10 x 24 Doric feet. 

Yet another pythagorean triangle inheres in the design of the 
temple (Figure 2). On the flank elevation such a triangle is formed 

Figure 2: SOUTH SIDE ELEVATION R. A. Baldwin 

with its base stretching along the top of the stylobate from the axis 
of one corner column to the axis of the column at the other end of 
the line, a distance of 96 Doric feet. The vertical side of the tri­
angle is formed by the lateral height of the temple from the top of 
the stylobate to the top of the sima. The height of the columns of 
the peristyle is 6.122 m. while the height of the entablature from 
the top of the abacus to the top of the sima is one-half this distance 
(3.062 m.).23 The sum of these two measurements is 9.184 m., 
precisely 28 Doric feet of 0.328 m. The precision of this figure is a 
persuasive argument that the architect intended the height of the 
temple from the top of the stylobate to the top of the sima to be 
28 Doric feet, since Krauss' careful measurements come to exactly 
this figure even though the top of the sima does not stand vertically 
over the axis of the peristyle columns. Seen from the side, the flank 
of a Greek temple is essentially a two-dimensional figure, and the 
top of the sima is the leading edge of its upper side. One can also 

22 cr. w. Sierpinski, Pythagorean Triangles, trans. A. Sharma (New York 1962) 1, 
11-14. 

23 Krauss (supra n.5) 2, 17, and Abb. 43. 



NED NABERS AND SUSAN FORD WILTSHIRE 213 

note that architects elsewhere have been concerned with express­
ing the height of temples either in whole numbers or as a multiple 
of the standard interaxial (although admittedly not to the top of 
the horizontal sima). In Temple A at Agrigentum the height of the 
temple to the corona is three times the basic interaxial, and in 
Temple D on that same site the same ratio exists between the stan­
dard interaxial and the height of the temple to the roof-edge. 24 In 
addition, as Dinsmoor pointed out, the height of the Parthenon 
from its stylobate to the top of the geison is precisely 42 Doric 
feet.25 The Parthenon, of course, has no horizontal sima. 

The number 28 may seem unexpected, but it is the equivalent of 
24 + 4, and it is also a 'perfect' number, the sum of all of its aliquot 
divisors or integral factors (1 + 2 + 4 + 7 + 14 = 28).26 Even 
more noteworthy is the fact that the hypotenuse of such a triangle 
is the square root of 10,000 (962 + 28 2 or 9216 + 784 = 10,000), 
which is 100. The perimeter of this triangle is 28 + 96 + 100, or 
224, which can also be resolved to 100 + 100 + 24. A triangle 
with the sides 28, 96, 100 is a version of the primitive pythagorean 
triangle 7, 24, 25, enlarged by a factor of 4. 

The occurrence of the crucial Pythagorean numbers four, ten, 
and twenty-four, repeated in the basic dimensions of the building, 
i.e., its height, breadth, and length (measured from column axis to 
column axis), leaves little room for doubt that their existence is 
intentional. Furthermore, it can hardly be sheer accident that the 
architect of the Athena temple created two pythagorean triangles 
in two major perspectives of its design using the three basic dimen­
sions of the temple. 27 

24 Gruben (supra n.lO) 437, 440-4l. 
25 Dinsmoor (supra n.11) 264. 
26 There is no evidence for such 'perfect' numbers in Greek theory before Euclid, al­

though Iamblichus (In Nic. p.35.1-7 Pistelli) attributes the discovery of 'friendly' (or 
'amicable') numbers to Pythagoras. Two numbers are 'friendly' if each is the sum of the 
aliquot divisors of the other; cf. Thomas Heath, A History of Greek Mathematics I (Oxford 
1921) 74-75. We are grateful to our colleague R. Dale Sweeney for his observation of 28 as 
a 'perfect' number. 

27 Our attempts to identify other Greek temples, western or mainland, which show the 
same sort of planning around Pythagorean concepts have been completely unsuccessful. To 
take the nearly contemporary Tavole Paladine at Metapontum as an example, using the 
figures from Lorenzen's tables (supra n.18) 146, and employing the Ionic foot of 0.295 m. 
established for this temple by Dinsmoor (supra n.l1) 358, we find the distances from the 
axis of one corner column to the axis of the other corner column 109.09 Ionic feet on the 
longer sides and 50.10 on the shorter. The hypotenuse would then equal 120.04 Ionic feet. 
Calculations from the dimensions of other temples yield similar fractional numbers. Even 



214 THE ATHENA TEMPLE AT PAESTUM 

We emphasize once again that we are using the precise measure­
ments of the temple independently established by Krauss and that 
it was he who suggested the Doric foot of 0.328 m. Nor have we 
rounded off figures more than to the nearest one-hundredth of a 
Doric foot. 28 We do not claim that Pythagorean ideas governed the 
design of the temple in every part, from the dimensions of its stylo­
bate down to the proportions of its guttae, but rather that its three 
basic dimensions and the triangles formed quite naturally from 
them display essential Pythagorean con,cepts of number theory. 
With this extension of the work of Kayser and especially of Hollo­
way, we may now be even more confident that the teachings of 
Pythagoras in southern Italy affected the design of the Athena 
temple.29 

It is impossible to reconstruct the relationship between philo­
sophical and political history in southern Italy during this period. 
We know that Croton devastated Sybaris in 510 B.c.,30 marking 
the expansion of Crotonian and thus probably of Pythagorean in­
fluence. Numismatic evidence for a 'Crotonian Alliance', examined 
by Kahrstedt31 and others, does not provide a reliable chronology, 
although von Fritz accepts Kahrstedt's main point, that Croton 
exercised considerable economic and political influence through 
much of southern Italy from the latter part of the sixth to about 

the peripteral temple of Apollo on Delos, which also has uniform interaxials all the way 
around its 6 by 13 peristyle, fails to achieve a pythagorean triangle. Since the interaxials are 
uniform, there does exist a triangle (measured from corner column axis to corner column 
axis again) in the plan which has the proportions of the 5, 12, 13 pythagorean triangle, but 
the sides of the triangle are not expressed in terms of even feet. The Pythagoreans con­
sidered only whole numbers to be numbers (Morris Kline, Mathematical Thought from 
Ancient to Modern Times [Oxford 1972] 32). The excavators determined that a foot of 
0.297 m. was used in the construction, with 7 11/16 feet to each interaxial: Fernand Courby, 
Les temples d'Apollon (Delos 12 [Paris 1931]) 93-95. This yields a length from corner 
column axis to corner column axis of 12 x 711/16 or 92% feet and a width of 5 x 711/16 or 
38 7/16 feet. The hypotenuse of such a triangle would be equal to the square root of 9987.504 
or 99.938 feet. This supports our contention that pythagorean triangles were not created by 
accident. 

28 For instance, when we state that the width of a corner triglyph (0.9885 m.) is 3 Doric 
feet, it will be found that 0.9855 -i- 0.328 = 3.004573171. 

29 Even though he is using other arguments, many of which are questionable, Lorenzen 
(supra n.18) 80 claims that the planning arrangement of temples in southern Italy was 
altered after the arrival of Pythagoras in Croton. In his careful study Bell (supra n.15) 368-
72 has argued persuasively that Pythagorean number theory influenced the design of the 
Olympieion at Akragas. 

30 Diod. 11.90. See T. J. Dunbabin, The Western Greeks (Oxford 1948) 362-65. 
31 U. Kahrstedt, "Zur Geschichte Grossgriechenlands im 5ten Jahrhundert," Hermes 53 

(1918) 180-87. 



NED NABERS AND SUSAN FORD WILTSHIRE 215 

the middle of the fifth_ century.32 Iamblichus (Vit.Pyth. 85) lists 
seven Pythagoreans active at Poseidonia (Paestum), although their 
dates cannot be determined. Pythagoreans must have been active 
at nearby Elea by the early fifth century, for their influence on 
Parmenides is well-attested. 33 Even so, it is by no means certain 
that Pythagoreans had political control of any Italian city at any 
time; von Fritz contends rather that leaders in various cities were 
attracted to Pythagorean principles and were influenced by them 
in their political activities. 34 

Given these questions about the nature and extent of Pythago­
reanism in southern Italy in the late sixth century, the evidence of 
the temple of Athena at Paestum takes on added significance. Here 
we have a structure of fairly certain date, contemporary with 
Pythagoras himself, which at least attests the Pythagorean con­
sciousness of its architect and may reflect broader philosophical 
and political conditions at Paestum as well. Finally, as a physical 
monument, it manifests in an empirical way the fundamental 
Pythagorean proposition that "things are numbers" and suggests 
that the cosmic order apparent to the Pythagoreans in the musical 
scale may also be expressed in architectural form. 

VANDERBILT UNIVERSITY 

August, I980 

32 Kurt von Fritz, Pythagorean Politics in Southern Italy (New York 1950) 85. 
33 For example, Diog.Laer. 9.21. See Minar (supra n.l) 40. 
34 Supra n.32: 95 ff.