# envelope

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Related to enveloped: Enveloped virus

## 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 ?
Erik sang like the god of thunder, sang a DIES IRAE that enveloped us as in a storm.
The mourners, too, enveloped and swathed in their skirts and gowns, were unable to bestir themselves, and so with entire safety to himself Don Quixote belaboured them all and drove them off against their will, for they all thought it was no man but a devil from hell come to carry away the dead body they had in the litter.
Till soon a dense fog enveloped the ship and all around her.
It made the round of the frigate, which was then making fourteen knots, and enveloped it with its electric rings like luminous dust.
This something was enveloped in a cloak, and D'Artagnan at first believed it was a man; but by the smallness of the form, the hesitation of the walk, and the indecision of the step, he soon discovered that it was a woman.
The latter article of dress was of great importance, since it enveloped the wearer's body nearly to the knees, and was perhaps bedizened with the amount of his whole year's income, in golden flowers and foliage.
This precious commodity they brought to the house, enveloped in multitudinous folds of leaves; and as a special mark of the esteem in which they held me, would spread an immense leaf on the ground, and dropping one by one a few minute particles of the salt upon it, invite me to taste them.
In one moment I've seen what has hitherto been Enveloped in absolute mystery, And without extra charge I will give you at large A Lesson in Natural History.
Exactly at a quarter to twelve he appeared under the lofty portal of the Hotel de Louvre, with his fresh face, his ill- fitting grey suit, and enveloped in his own sympathetic atmosphere.
Turn what way she would, they surrounded, enveloped and pounded down upon her.
And here are Moorish women who are enveloped from head to foot in coarse white robes, and whose sex can only be determined by the fact that they only leave one eye visible and never look at men of their own race, or are looked at by them in public.
The eye took in nothing but one vast ocean of flame; the large trees stood forth in black relief in this huge furnace, their branches covered with glowing coals, while the whole blazing mass, the entire conflagration, was reflected on the clouds, and the travellers could fancy themselves enveloped in a hollow globe of fire.

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