Envelope of A Family of Surfaces
A one-parameter family of surfaces in three-dimensional Euclidean space is given by a set of equations
depending on a real parameter a. For example the tangent planes to a surface along a curve in the surface form such a family.
Two surfaces corresponding to different values a and a' intersect in a common curve defined by
In the limit as a' approaches a, this curve tends to a curve contained in the surface at a
This curve is called the characteristic of the family at a. As a varies the locus of these characteristic curves defines a surface called the envelope of the family of surfaces.
The envelope of a family of surfaces is tangent to each surface in the family along the characteristic curve in that surface.
Read more about this topic: Envelope (mathematics)
Famous quotes containing the words envelope, family and/or surfaces:
“Geroge Peatty: I’m gonna have it, Sherry. Hundreds of thousands, maybe a half million.
Sherry Peatty: Of course you are, darling. Did you put the right address on the envelope when you sent it to the North Pole?”
—Stanley Kubrick (b. 1928)
“What we often take to be family values—the work ethic, honesty, clean living, marital fidelity, and individual responsibility—are in fact social, religious, or cultural values. To be sure, these values are transmitted by parents to their children and are familial in that sense. They do not, however, originate within the family. It is the value of close relationships with other family members, and the importance of these bonds relative to other needs.”
—David Elkind (20th century)
“But ice-crunching and loud gum-chewing, together with drumming on tables, and whistling the same tune seventy times in succession, because they indicate an indifference on the part of the perpetrator to the rest of the world in general, are not only registered on the delicate surfaces of the brain but eat little holes in it until it finally collapses or blows up.”
—Robert Benchley (1889–1945)