# Developable surface

From Diffgeom

This article defines a property that makes sense for a surface embedded in , viz three-dimensional Euclidean space. The property is invariant under orthogonal transformations and scaling, i.e., under all similarity transformations.

View other such properties

## Contents

## Definition

A surface embedded in is termed **developable** if it satisfies both these conditions:

- It is a ruled surface
- Its Gaussian curvature is everywhere zero, viz it is a flat surface

Equivalently, a surface is developable if it can be generated by a one-parameter family of lines.