A dome subjected to compression forces: A comparison study between the mathematical model, the catenary rotation surface and the paraboloid

Singular minimal surfaces are models in architecture of domes where compression forces are the only ones acting on the dome. This paper investigates if catenary rotation surfaces and paraboloids are good candidates to substitute the singular minimal surfaces as designs for the construction of domes. Assuming that these surfaces have the same surface area and the same boundary curve, a numerical comparison of the heights of their centers of gravity and the curvatures is presented. This method is performed with Mathematica together with an analysis based on the slope linear regression line. The numerical results demonstrate that the centers of gravity of the two candidates are considerably close to that of the mathematical model. It is also proved that the paraboloids adjust better than catenary rotation surfaces. •Ideal models of domes are not computable by quadratures.•Catenary rotation surfaces and paraboloids are good approximations of domes.•Centers of gravity of paraboloids and rotational tectums are almost identical.•Paraboloids adjust better catenary rotation surfaces to the ideal model.