developable surface

The following discussion of developable surfaces is based on that concept.

The cylinder, cone and of course the plane are all developable surfaces.

There are developable surfaces in R which are not ruled.

The developable surfaces which can be realized in three-dimensional space include:

Until that time, the only known developable surfaces were the generalized cones and the cylinders.

Curved origami allows the paper to form developable surfaces that are not flat.

Because of this, many developable surfaces can be visualised as the surface formed by moving a straight line in space.

Developable surface is a surface isometric to the plane.

In three dimensions all developable surfaces are ruled surfaces.

Spheres are not developable surfaces under any metric as they cannot be unrolled onto a plane.

In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature).

While the first step inevitably distorts some properties of the globe, the developable surface can then be unfolded without further distortion.

A developable surface in geometry.

Developable surfaces have several practical applications.

The developable surface may also be either tangent or secant to the sphere or ellipsoid.

The three developable surfaces (plane, cylinder, cone) provide useful models for understanding, describing, and developing map projections.

Such surfaces are called developable surfaces.

Formally, in mathematics, a developable surface is a surface with zero Gaussian curvature.

Most smooth surfaces (and most surfaces in general) are not developable surfaces.

The sphere and ellipsoid do not have developable surfaces, so any projection of them onto a plane will have to distort the image.

Moving the developable surface away from contact with the globe never preserves or optimizes metric properties, so that possibility is not discussed further here.

A developable surface is a surface that can be (locally) unrolled onto a flat plane without tearing or stretching it.

More generally, any developable surface in three dimensions is part of a complete ruled surface, and so itself must be locally ruled.

Tangent developable surfaces; which are constructed by extending the tangent lines of a spatial curve.

The Gauss curvature of a Frenet ribbon vanishes, and so it is a developable surface.