What is the Shape of a Cupola?

TL;DR

This paper explores the shape of a surface formed by hanging flexible material with fixed boundary, modeling cupolas, and introduces a novel roof design with a horizontal axis of revolution.

Contribution

It provides a new geometric model for cupolas based on hanging surfaces and proposes a unique roof design with a horizontal axis of symmetry.

Findings

Shape of hanging surface models cupolas

Introduction of a novel roof design with horizontal axis of revolution

Illustration of rotational examples for architectural applications

Abstract

This article examines the shape of a surface obtained by a hanging flexible, inelastic material with prescribed area and boundary curve. The shape of this surface, after being turned upside down, is a model for cupolas (or domes) under the simple hypothesis of compression. Investigating the rotational examples, we provide and illustrate a novel design for a roof which has the extraordinary property that its shape, although natural, is modeled by a surface of revolution whose axis of rotation is horizontal.