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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


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.



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).


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.


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.
The glass or metal housing of an electron tube or the glass housing of an incandescent lamp.
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.
The outer membranous lipoprotein coat of certain viruses. Also known as bulb.


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.


(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.

(3) See also pushing the envelope.


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 periodicals archive ?
Many of E-Stamp's beta customers have requested and are using these envelopes, finding that the E-Stamp window envelopes are a significant time-saver.
If we had kept to their requirements, we would have been unable to fit the cards inside window envelopes, with the consequence that many thousands of pounds extra would have to have been spent on labels, larger envelopes and extra postage.
EzCheckprinting software offers customers more bang for their buck with backup and restore feature, check customization for window envelopes, and many other money saving options for customers.
Rather than a tale of two cities, this is a tale of two DM packages from the same city, Boston, both arriving in the mail on the same day, both in white 9 X 12-inch window envelopes, and both soliciting subscriptions to health newsletters.
Plus, RISO's high-speed inkjet printers utilize a heatless printing process that allows the system to accommodate window envelopes, and alleviates the stress of flaps adhering during printing or problems with pressure sensitive envelope stocks.
Tenders are invited for Supply of Window Envelopes for despatch of Telephone/Mobile/CDMA Bills in Nashik SSA of BSNL
com's mailing and window envelopes can also be personalized to feature company logos at no extra cost.
The company also uses soy inks in its printing, manufactures biodegradable and compostable window envelopes, and has a full line of recycled and post-consumer waste content products.
Tenders are invited for For Supply Of Window Envelopes For Dispatch Of Telephone/Mobile/Cdma Bills, In Nashik Ssa Of Bsnl Eligibility Criteria : The bidders shall submit necessary documentary proof showing that they meet the eligibility criteria as applicable or whichever is required as per terms and conditions stipulated in tender document along with their tender bid.
Tenders are invited for Supply Of Software Based Pre Printed Mobile Bill Forms And Window Envelopes In Lucknow Ssa
This solution increased productivity and reduced costs by eliminating the need for window envelopes and printing duplex to add the individual's address.
Additionally, customers who print stamps directly onto a document while using Word will be able to mail the document in one of E-Stamp's patented window envelopes, which features a special "window" for the digital stamp, after the U.