---
tag: YKVHDB52XW
kind: concept
name: Developable surface
msc: [53A05]
specializes: [6080X3FAD4]
sources:
  - url: https://en.wikipedia.org/wiki/Developable_surface
same_as:
  wikidata: Q336298
  wikipedia: Developable surface
---

## Summary

A developable surface is a surface in space whose Gaussian curvature is zero at every point.
Such a surface can be flattened onto a plane, at least locally, without stretching or tearing.
Cylinders, cones and the surfaces swept by the tangent lines of a space curve are the basic examples.
They matter in practice because they are the shapes one can bend out of a flat sheet of paper or metal.

## Explanations

### L1 human

Roll a sheet of paper into a tube or a cone: you get a developable surface.
No length on the paper changes when you do this, so you can unroll it flat again.
A sphere is not developable, which is why every flat map of the Earth distorts some distances.
The number that decides this is the Gaussian curvature: it is zero on a cylinder and positive on a sphere.