History of 18th century early modern domes

Early modern domes built in the 18th century benefited from the newly developed mathematics of calculus and the study of statics. There were numerous studies on the catenary curve as the most stable form for arches and vaults and the ideal shape for a dome was debated in the late 18th century. Calculus allowed Guarini's experimental designs with intersections of spheres, barrel vaults, and oval domes to be proven and they would become the foundation of Rococo spatial arrangements.

In the areas of the Holy Roman Empire, rebuilding of the many palaces and churches destroyed in the Thirty Years' War had begun by the end of the seventeenth century. Ovals resolved the tension between longitudinal and centralized spaces in German Baroque architecture, but resting them on drums created problems and so the domes often rested directly on arches or pendentives. Bulbous domes were popular in central and southern Germany and in Austria in the 18th century, and influenced those in Poland and Eastern Europe in the Baroque period. However, many bulbous domes in the larger cities of eastern Europe were replaced during the second half of the eighteenth century in favor of hemispherical or stilted cupolas in the French or Italian styles.

Domes in Mexico were single shell constructions, with few exceptions, and the domes and lanterns were commonly covered with glazed tiles. A wooden structure supporting a layer of earth fill to support the domes during construction, a technique used in Europe to build domes since the Romanesque era.

Although never very popular in domestic settings, domes were used in a number of 18th century homes built in the Neoclassical style. In the United States, small cupolas were used to distinguish public buildings from private residences. After a domed design was chosen for the national capitol, several states added prominent domes to their assembly buildings.