Funicular
Three forces must meet at a point, and a drawing can find it
A body held by exactly three forces has their lines of action concurrent. That is a theorem, it is enough to solve for direction and magnitude, and for a century it was done with a straightedge.
The shape that carries itself, and the arch that is its reflection
Hang a chain and it takes the one shape that carries its load in pure tension. Turn the shape upside down and it carries the same load in pure compression. That is what an arch is.
The polygon that finds the shape
A hanging string under five loads has no smooth curve in it — it has five vertices and six straight segments, and every slope in it is a running sum divided by one number.
The line that must stay inside
A masonry arch does not stand because its shape is right. It stands because some line of compression can be drawn inside the stonework — any one will do, and there are infinitely many to choose from.
Named alongside it
The objects these essays reach for when they reach for this one.
Horizontal thrustThrust lineForm findingSag ratioCatenaryConcurrencyForce polygonFree body diagramFunicular polygonGeometrical factor of safetyGraphic staticsHinge