“Tangential developable”的意思、由来-开放百科全书

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Tangential developable

释义

References

In the mathematical study of the differential geometry of surfaces, a tangential developable is a particular kind of developable surface obtained from a curve in Euclidean space as the surface swept out by the tangent lines to the curve. Such a surface is also the envelope of the tangent planes to the curve.

With the exceptions of the plane, a cylinder, and a cone, every developable surface in three-dimensional Euclidean space is the tangential developable of a certain curve, the edge of regression. This curve is obtained by first developing the surface into the plane, and then considering the image in the plane of the generators of the ruling on the surface. The envelope of this family of lines is a plane curve whose inverse image under the development is the edge of regression. Intuitively, it is a curve along which the surface needs to be folded during the process of developing into the plane.

References

{{citation|title=Lectures on Classical Differential Geometry|first=Dirk Jan|last=Struik|publisher=Addison-Wesley|year=1961}}.
{{Citation | last1=Hilbert | first1=David | author1-link=David Hilbert | last2=Cohn-Vossen | first2=Stephan | author2-link=Stephan Cohn-Vossen | title=Geometry and the Imagination | publisher=Chelsea | location=New York | edition=2nd | isbn=978-0-8284-1087-8 | year=1952 }}
{{springer|first=I.Kh.|last=Sabitov|year=2001|title=Developable surface|id=d/d031430}}
{{springer|first=M.I.|last=Voitsekhovskii|year=2001|title=Edge of regression|id=e/e035050}}

1 : Differential geometry of surfaces

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