# envelope

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Related to enveloping: get along, hold off, wreak havoc, Pertaining to

## envelope

1. Biology any enclosing structure, such as a membrane, shell, or skin
2. the bag enclosing the gas in a balloon
3. Maths a curve or surface that is tangent to each one of a group of curves or surfaces
4. Electronics the sealed glass or metal housing of a valve, electric light, etc.
5. Telecomm the outer shape of a modulated wave, formed by the peaks of successive cycles of the carrier wave

## Envelope

The boundary that separates a building’s conditioned and unconditioned spaces. The term usually refers to heat and air transfer, such as through walls, windows, and the roof. All of these are part of the building’s envelope. Also, the imaginary shape of a building indicating its maximum volume; used primarily to check the plan, setback, and other restrictions regarding zoning regulations.

## Envelope

of a family of curves in a plane (or of surfaces in space), a curve (or surface) that touches at each of its points a single curve (or surface) of the family and is geometrically different from that curve (or surface) in an arbitrarily small neighborhood of the point of contact. The equation of the envelope of a plane family of curves defined by the equation f(x, y, C) = 0, which contains a parameter C, can be obtained by eliminating C from the system of equations

Here it is assumed that f(x, y, C) has continuous partial derivatives of the first order with respect to all three arguments. In general, this elimination yields not only the envelope but also the locus of the singular points of the curves of the family, that is, the points for which f″x and f″y, vanish simultaneously.

Figure 1

The following are examples in the plane. (1) The family of circles of radius R whose centers lie on a line has as an envelope a pair of lines parallel to the line of the centers and located at a distance R from that line (see Figure 1). (2) Any curve is the envelope of the family of its tangents and of the family of its circles of curvature. (3) The envelope of the family of normals to a given curve is its evolute (the evolute of an ellipse is shown in Figure 2).

Figure 2

The envelope of a family of surfaces in space may touch each member of the family at a point or along a curve.

For example, (1) the envelope of a family of spheres of radius R with centers lying on a single line is a circular cylinder of radius R whose axis is that line (the cylinder touches each sphere along a circle); (2) the envelope of a family of spheres of radius R whose centers lie in a single plane is a pair of planes parallel to the plane of the centers and located at a distance R from that plane (the planes forming the envelope touch each sphere in a point).

The concept of an envelope has significance not only in geometry but also in certain problems in mathematical analysis (singular solutions in the theory of differential equations) and theoretical physics (the caustic and the wave front in optics).

### REFERENCES

Tolstov, G. P. “K otyskaniiu ogibaiushchei semeistva ploskikh krivykh.” Uspekhi matematicheskikh nauk, 1952, vol. 7, no. 4.
La Vallée Poussin, C. J. de. Kurs analiza beskonechno malykh, vol. 2. Leningrad-Moscow, 1933. (Translated from French.)
Il’in, V. A., and E. G. Pozniak. Osnovy matematicheskogo analiza, 3rd ed., part 1. Moscow, 1971.

## envelope

[′en·və‚lōp]
(communications)
A curve drawn to pass through the peaks of a graph, such as that of a moduated radio-frequency carrier signal.
(cell and molecular biology)
The sum of all cell-surface elements that are located outside the plasma membrane.
(engineering)
The glass or metal housing of an electron tube or the glass housing of an incandescent lamp.
(mathematics)
The envelope of a one-parameter family of curves is a curve which has a common tangent with each member of the family.
The envelope of a one-parameter family of surfaces is the surface swept out by the characteristic curves of the family.
(virology)
The outer membranous lipoprotein coat of certain viruses. Also known as bulb.

## envelope

1. The imaginary shape of a building indicating its maximum volume; used to check the plan and setback (and similar restrictions) with respect to zoning regulations.
2. The folded-over, continuous edge formed by turning the lowest ply of a built-up roofing membrane over the top surface layer; prevents bitumen from dripping through the exposed edge joints and seepage of water into the insulation.

## envelope

(1) A range of frequencies for a particular operation.

(2) A group of bits or items that is packaged and treated as a single unit.

## Envelope

(dreams)
Mail or letters usually come in envelopes. When we see envelopes in our dreams, we are typically dreaming about receiving news, information, or messages from someone specific or from the world at large. If you are the individual that looks forward to mail, this dream may be positive. However, if you dread the envelopes that typically hold the monthly bills, then this dream may have negative and anxiety provoking symbolism. Typically, however, dreaming about receiving letters has positive and at times spiritual connotations. You may be coming into awareness about some aspect of your life where you make new realizations and get to the “truth” of things. Some believe that seeing many unopened envelopes in your dreams may represent missed opportunities.
References in classic literature ?
And then hard upon this little rattle of shots and bombs came, all about him, enveloping him, engulfing him, immense and overwhelming, a quivering white blaze of lightning and a thunder-clap that was like the bursting of a world.
Her mind and body both seemed to have floated into another region of quick-sailing clouds rapidly passing across each other and enveloping everything in a vaporous indistinctness.
Should this enveloping force be interrupted in any direction a delicate instrument immediately apprehends the irregularity, at the same time imparting an impulse to a magnetic device which in turn actuates the steering mechanism, diverting the bow of the flier away from the obstacle until the craft's radio-activity sphere is no longer in contact with the obstruction, then she falls once more into her normal course.
For an hour I battled against the cruelly enveloping death that surrounded me upon all sides.
It could never be the same, of course, but yet, day by day, she found her mother-love, enveloping the waif more closely until she sometimes sat with closed eyes lost in the sweet imagining that the little bundle of humanity at her breast was truly her own.
Moving through the sunlit garden at the side of the great Warlord, the scintillant rays of his countless gems enveloping him as in an aureole of light imparted to his noble figure a suggestion of godliness.
said Isay, enveloping Nikita in the odour of the vodka he had drunk.
ghost adds something of the mystery enveloping a farmer from another
During the entire incident his shouts and curses were heard, as if through an enveloping uproar of such sounds of rage and fury as I had never heard from the throat of man or brute!
Spenser strangely planned to narrate this beginning of the whole in his final Book, but even if it had been properly placed at the outset it would have served only as a loose enveloping action for a series of stories essentially as distinct as those in Malory.
But Marlow was not typical(if his propensity to spin yarns be excepted), and to him the meaning of an episode was not inside like a kernel but outside, enveloping the tale which brought it out only as a glow brings out a haze, in the likeness of one of these misty halos that sometimes are made visible by the spectral illumination of moonshine.

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