A chain hanging freely takes the one shape in which it is in pure tension; turn that shape upside down and it is the shape of an arch in pure compression for the same loads.
free-hanging chain (catenary) ↔ ideal arch under its own weight
Rules · Plans · Geometry · Optics
The ellipse belongs inside
Use the elliptical plan chiefly for interiors, where the whole curve is seen at once; on the outside of any but a very large building its changing curvature looks like a distorted circle, and the circle is better.
The Romans, Stratton notes, confined the ellipse to the amphitheatre, while French architects of the seventeenth and eighteenth centuries developed it in rooms, vestibules and staircases. Inside, it lets a curved room lie along a cross axis or fill a space too long for a circle.
Yet he holds that the unbroken horizontal lines of a truly circular interior, as in the Pantheon, can hardly be bettered.
Related rules
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
To combine the unity of a central plan with the direction a church needs, plan the space as an oval, set across the axis to widen the view of the altar, or along it to lead the eye towards it.
Divide the inside of a dome into coffers that shrink in step with the meridians as they rise, so that their perspective deepens the dome and draws the eye to the light of the lantern.
Let the wall of a façade curve in plan (concave, convex, concave) so that the front answers the street, the light and the space within, and the order bends with it.
Make the stair of a palace a processional space: one broad flight rising to a landing, then turning back in two flights either side to arrive at the principal floor beneath a single great vault.
Cite this page Chris Paton, “The ellipse belongs inside”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/stratton-ellipse-inside. Text, drawings and models licensed under CC BY-NC 4.0.