Catenary arch

The 17th-century scientist Robert Hooke wrote: "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum", or, "As hangs a flexible cable so, inverted, stand the touching pieces of an arch.

"[4] A note written by Thomas Jefferson in 1788 reads, "I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni.

[9][10] This principle has been employed architecturally to create arched structures that follow exactly, and in a visibly apparent way, the form of an inverted catenary.

The catenary, spun 180 degrees, forms the structure of simple domed building such as the beehive homes of the Dingle Peninsula, Ireland.

Buildings that have heavy roofs that are arched in shape and deliver a strong outward thrust must comply with the form of the catenary curve in order not to collapse.

In the 15th century Brunelleschi designed the pointed, octagonal, Gothic dome on Florence Cathedral in a manner that utilised the principle of the catenary arch.

[citation needed] In the 17th century, Christopher Wren designed the dome of St Paul's Cathedral based directly on a catenary curve.

[31][23] This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow.

[32] The Nubian ton is a burial vault, of Nubia, For greatest stability, the structure’s cross-section follows a catenary arch.