Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.
Rules · Plans · Geometry · Use
The Roman theatre: four triangles
Draw the orchestra circle and inscribe in it four equilateral triangles at equal intervals; the side nearest the scene fixes the front of the scaena, a parallel through the centre fixes the front of the stage, and the angles on the auditorium side give the directions of the stairways.
12 vertices at 30°: 7 fix the stairs of the lower cavea, 5 fix the doors and passages of the scene; stage depth = r⁄2
Vitruvius likens the figure to the diagram astrologers draw of the twelve signs of the zodiac. Its twelve points do double duty: seven on the auditorium side mark the stairways between the wedges of seats (cunei) up to the first cross-aisle, with the upper stairs set midway between them; five on the scene side mark the royal door in the centre, the doors of the guest chambers either side, and the passages at the ends.
Because the side of an inscribed equilateral triangle lies half a radius from the centre, the Roman stage is deep: a platform for all the performers, since the orchestra itself was given over to the seats of senators. The steps are to be between a foot and a palm and a foot and six fingers high, and two to two and a half feet deep.
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Cite this page Chris Paton, “The Roman theatre: four triangles”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/theatre-four-triangles. Text, drawings and models licensed under CC BY-NC 4.0.