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back-of-the-envelope calculation

A calculation or mathematical formulation that is approximated in a quick, informal, and rough manner, as might be sketched out on a scrap of paper (such as the back of an envelope). When it came time to pay the bill, we had to do some back-of-the-envelope calculations to figure out who owed how much.

the opening of an envelope

Any event, celebration, or ceremony, no matter how trivial or unremarkable, that one attends purely for the sake of visibility. Often said in relation to celebrities or media personalities who make a point of attending anything that will give them more public exposure. In a bid to cultivate a media buzz around herself, the Internet sensation has been to the openings of films, book launches, and celebrity galas. With the way she carries on, she'd even go to the opening of an envelope!
See also: envelope, of, opening

envelop (oneself, someone, or something) in (something)

To wrap oneself, someone, or something in something. As soon as I got in from the cold, I enveloped myself in a blanket and sat in front of the fire. The snowstorm enveloped our area even faster than predicted with white-out conditions.
See also: envelop

push the envelope

To expand on, exceed, or test the limits of the established norm or standard. The company is renowned for pushing the envelope whenever they develop a new piece of technology. If you want to make a name for yourself in the art world, then you can't be afraid of pushing the envelope. It's a natural stage for most teenagers to push the envelope of their parents' rules.
See also: envelope, push

on the back of an envelope

Calculated, prepared, or drafted in an overly quick, informal, or rough manner, as might be scribbled on a scrap of paper (such as the back of an envelope). It seems clear that they devised this legislation on the back of an envelope. Now, don't come up with these figures on the back of an envelope—I want you to be thorough and double check each sum and calculation.
See also: back, envelope, of, on

push the envelope

Fig. to expand the definition, categorization, dimensions, or perimeters of something. The engineers wanted to completely redesign the product, but couldn't push the envelope because of a very restricted budget.
See also: envelope, push

push the envelope

Exceed the limits of what is normally done, be innovative, as in They are pushing the envelope in using only new fabrics for winter clothing. This idiom comes from aviation, the envelope alluding to the technical limits of a plane's performance, which, on a graph, appear as a rising slope as limits of speed and stress are approached and falls off when the capacity is exceeded and the pilot loses control; safety lies within these limits, or envelope, and exceeding them exposes pilot and plane to risk. [Slang; late 1960s]
See also: envelope, push

on the back of an envelope

If a piece of work was written or planned on the back of an envelope, it was prepared too quickly, with little thought or care. These proposals were sketched out on the back of an envelope. The screenplay sounds as if it's been written on the back of an envelope. Note: You can also talk about a back-of-an-envelope calculation or account to talk about something that is not accurate. According to his back-of-an-envelope calculation, a solar square of mirrors of this size would provide enough energy to supply the whole state.
See also: back, envelope, of, on

push the envelope

If you push the envelope, you do something to a greater degree or in a more extreme way than it has been done before. We have to keep pushing the envelope, trying new technologies and developing better methods. There's a valuable place for fashion and design that pushes the envelope a bit. Note: Rather than referring to stationery, the sense of envelope here is probably the one used to refer to the shape of a wave in electronics or a curve in mathematics. Pushing or stretching the envelope suggests changing the properties of the wave or curve.
See also: envelope, push

push the envelope (or the edge of the envelope)

approach or extend the limits of what is possible. informal
This expression was originally aviation slang and related to graphs of aerodynamic performance on which the envelope is the boundary line representing an aircraft's capabilities.
1993 Albuquerque These are extremely witty and clever stories that consistently push the envelope of TV comedy.
See also: envelope, push

push the ˈenvelope

do something in an extreme way in order to find out to what degree something is possible: Advertisements seem to be pushing the envelope of taste every day.People these days like to push the envelope with extreme sports. ▶ ˈenvelope-pushing noun, adj.: envelope-pushing technologyThis expression comes from the aeroplane industry. A plane’s envelope was the limit of its performance. Test pilots would need to push (the edge of) the envelope to see what the plane could and could not do.
See also: envelope, push

push the envelope

To exceed or try to exceed the existing limits of a discipline or activity.
See also: envelope, push
References in classic literature ?
With a firm, steady-eyed impudence, which seemed to hold back the threat of some abominable menace, he would proceed to sell over the counter some object looking obviously and scandalously not worth the money which passed in the transaction: a small cardboard box with apparently nothing inside, for instance, or one of those carefully closed yellow flimsy envelopes, or a soiled volume in paper covers with a promising title.
The envelope was addressed in the little attorney's handwriting.
No," replied Ginger, who had opened the envelope, "it is the rates and taxes, L 3 19 11 3/4 .
A little after, he got to his feet very sore and shaken, the poorer by a purse which contained exactly one penny postage- stamp, by a cambric handkerchief, and by the all-important envelope.
As soon, however, as the marquise had disappeared, her envious enemy, not being able to resist the desire to satisfy herself that her suspicions were well founded, advanced stealthily towards it like a panther and seized the envelope.
I took up the envelope and saw scrawled in red ink upon the inner flap, just above the gum, the letter K three times repeated.
You will kindly show the envelope of this letter to my man, Austin, when you call, as he has to take every precaution to shield me from the intrusive rascals who call themselves `journalists.
Such an envelope as this could retain the inflating fluid for any length of time.
How strange it seemed that to a full-grown white man an envelope was a mystery.
Denisov, frowning, took the envelope and opened it.
the captain asked, tearing open the envelope and moving a little nearer the electric light which shone out from the smoking room.
He saw nothing but the marking upon that letter, growing larger and larger as he gazed, the veritable writing of fate pressed upon the envelope by a rubber stamp--by the hand, perchance, of a clerk--"Opened by Censor.
I believe," he said, holding it out towards him, "that this envelope is yours.
He folded them just so, put the proper stamps inside the long envelope along with the manuscript, sealed the envelope, put more stamps outside, and dropped it into the mail-box.
The two inclosures had been secured in a sealed envelope, directed to the cottage.