Editing Ancient Greek architecture (section)

==== Proportion and optical illusion ====
The ideal of proportion that was used by ancient Greek architects in designing temples was not a simple mathematical progression using a square module. The math involved a more complex geometrical progression, the so-called [[Golden ratio|golden mean]]. The ratio is similar to that of the growth patterns of many spiral forms that occur in nature such as rams' horns, [[nautilus]] shells, fern fronds, and vine tendrils and which were a source of decorative motifs employed by ancient Greek architects as particularly in evidence in the volutes of capitals of the Ionic and Corinthian Orders.<ref name=BF15>{{harvnb|Fletcher|1996|p=126}}.</ref>

:<math> \frac 1 \varphi = \varphi - 1;\; \varphi = \frac{1 + \sqrt{5}}{2} \approx 1.618 </math>

The ancient Greek architects took a philosophic approach to the rules and proportions. The determining factor in the mathematics of any notable work of architecture was its ultimate appearance. The architects calculated for perspective, for the optical illusions that make edges of objects appear concave and for the fact that columns that are viewed against the sky look different from those adjacent that are viewed against a shadowed wall. Because of these factors, the architects adjusted the plans so that the major lines of any significant building are rarely straight.<ref name="BF15" /> The most obvious adjustment is to the profile of columns, which narrow from base to top. However, the narrowing is not regular, but gently curved so that each column appears to have a slight swelling, called ''entasis'' below the middle. The ''entasis'' is never sufficiently pronounced as to make the swelling wider than the base; it is controlled by a slight reduction in the rate of decrease of diameter.<ref name="BF3" />

{{multiple image
|align     = center
|direction = horizontal
|header_align = center
|header    =
|image1    = Parthenon-uncorrected.jpg
|width1    = 183
|alt1      =
|caption1  = The main lines of the Parthenon are all curved.
|image2    = 
|width2    = 176
|alt2      =
|caption2  = Diagram showing the optical corrections made by the architects of the Parthenon
|image3    = NautilusCutawayLogarithmicSpiral.jpg
|width3    = 182
|alt3      =
|caption3  = A sectioned [[nautilus]] shell. These shells may have provided inspiration for voluted Ionic capitals.
|image4    = Golden spiral in rectangles.svg
|width4    = 222
|alt4      =
|caption4  = The growth of the nautilus corresponds to the Golden Mean
}}
The [[Parthenon]], the Temple to the Goddess [[Athena]] on the [[Acropolis]] in Athens, is referred to by many as the pinnacle of ancient Greek architecture. [[Helen Gardner (art historian)|Helen Gardner]] refers to its "unsurpassable excellence", to be surveyed, studied and emulated by architects of later ages. Yet, as Gardner points out, there is hardly a straight line in the building.<ref name="HG4" /> [[Banister Fletcher]] calculated that the ''stylobate'' curves upward so that its centres at either end rise about {{convert|2.6|inch|mm|round=5|order=flip|abbr=off}} above the outer corners, and {{convert|4.3|inch|mm|order=flip|abbr=on}} on the longer sides. A slightly greater adjustment has been made to the entablature. The columns at the ends of the building are not vertical but are inclined towards the centre, with those at the corners being out of plumb by about {{convert|2.6|inch|mm|round=5|order=flip|abbr=on}}.<ref name="BF3" /> These outer columns are both slightly wider than their neighbours and are slightly closer than any of the others.<ref name=MFW2>{{harvnb|Moffett|Fazio|Wodehouse|2003|pp=50–53}}.</ref>{{clear}}