Plan the principal hall as a long rectangle entered on its short side through a porch with two columns between the side walls and a vestibule, and put a great round hearth in the centre of the hall, ringed by four columns carrying a raised roof.
Rules · Plans · Geometry · Use
The Greek theatre: three squares
Plan a Greek theatre by inscribing three squares in the orchestra circle; the side nearest the scene fixes the front of the stage (proscaenium), and the scene is set back to a line tangent to the circle.
proscaenium at r cos 45° ≈ 0.71 r from the centre; logeion 10–12 ft high
Vitruvius contrasts the Greek plan with the Roman: where the Roman has four triangles, the Greek has three squares, so the Greek orchestra is roomier, the stage (the logeion) is narrower and much higher, and the scene building stands further back. The reason is use: in the Greek theatre the chorus performed in the orchestra and only the actors on the stage.
Beyond the diameter the seats of the Greek cavea continue, following arcs struck from the ends of the diameter, so that the auditorium wraps more than a semicircle round the orchestra, as it does at Epidauros. The figure simplifies these arcs to a single centre.
Related rules
Do not lay the stylobate dead level: raise it gently toward the middle of each side, for a perfectly flat platform looks to the eye as if it sagged.
Parthenon: rise ≈ 11 cm over 69.5 m (flanks), ≈ 6.5 cm over 30.9 m (fronts), about 1 : 600
Give the shaft a continuous convex curve from base to necking, departing from a straight taper by only a few hundredths of a diameter, so that the column seems to flex under its load rather than to pinch.
Parthenon: greatest departure ≈ 1.7 cm on a shaft 9.6 m high (≈ 1⁄110 D)
A Doric frieze cannot obey all three of its rules at a corner: triglyphs over the column axes, a triglyph turning the corner, and metopes as broad as they are high. One of them must give way.
displacement of the corner triglyph = e − t⁄2 (e = half-depth of the architrave, t = triglyph width)
Let one simple ratio govern the whole: at the Parthenon the lower diameter is to the axial spacing, the width of the stylobate to its length, and the height of the order to the width of the front, all very nearly as 4 is to 9.
D : axial spacing ≈ 1.905 : 4.296 ≈ 4 : 9; stylobate 30.88 : 69.50 ≈ 4 : 9
In a peripteral temple the flanks have twice as many intercolumniations as the front: six columns in front means eleven along each side, counting the corner columns twice.
side columns = 2n − 1 (Vitruvius) · 2n + 1 (Greek practice)
Cite this page Chris Paton, “The Greek theatre: three squares”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/greek-theatre-three-squares. Text, drawings and models licensed under CC BY-NC 4.0.