# envelope

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## 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
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## 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.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.

## 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.

Copyright © 1981-2019 by The Computer Language Company Inc. All Rights reserved. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher.

## 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.
Bedside Dream Dictionary by Silvana Amar Copyright © 2007 by Skyhorse Publishing, Inc.
References in periodicals archive ?
In a press release, the hospital said that the study found positive results and demonstrated that the envelope reduced the risk of major infection by 40 percent, and pocket infection by 61 percent, in patients at increased risk for infections receiving CIEDs, compared to standard-of-care pre-operative antibiotics.
"The golden envelopes won't be that hard to find, but shoppers just need to keep their eyes peeled and when they find one of the envelopes, all they need to do is take it to our customer services desk to claim their intu Gift Card."
For those who don't remember last year's mix-up, the wrong envelope for best picture was handed to Warren Beatty and Faye Dunaway.
The acquisition expands the geographical footprint of Encore Envelopes, which is the UK's largest independently-owned printed envelope maker.
The characteristic information on bearing faults is contained in the envelope of the extracted impulses.
Summary: Suspect took two envelopes that contained foreign currency collected as donations to the needy
Keywords: Envelope curve; PMF; Gumbel method; Log Pearson Type-III; Two parameter gamma.
The envelope was sent to Thomas Barron, of Ravensknowle Road, from Kuruman in what is now South Africa by Trooper Frank Lewin, of the 8th Battalion Imperial Yeomanry.
The Building Envelope course series includes information on the proper inspection and investigation of building envelope issues such as (but not limited to) water intrusion and latent construction defects.
I am trying to open an envelope. No, seriously, you are knocking into my leg.
Fold the flap of another envelope backwards, as shown, and place that envelope on the face of the envelope containing the flowers.
Everybody in the profession should know and observe The Rule of Envelope Copy.

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