# approximation

## Definitions

• WordNet 3.6
• n approximation the act of bringing near or bringing together especially the cut edges of tissue
• n approximation the quality of coming near to identity (especially close in quantity)
• n approximation an approximate calculation of quantity or degree or worth "an estimate of what it would cost","a rough idea how long it would take"
• n approximation an imprecise or incomplete account "newspapers gave only an approximation of the actual events"
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Webster's Revised Unabridged Dictionary
• Interesting fact: Approximately 850 peanuts make a 18 oz jar of peanut butter
• Approximation (Math) A continual approach or coming nearer to a result; as, to solve an equation by approximation .
• Approximation (Math) A value that is nearly but not exactly correct.
• Approximation An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc.
• Approximation The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating. "The largest capacity and the most noble dispositions are but an approximation to the proper standard and true symmetry of human nature."
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Century Dictionary and Cyclopedia
• Interesting fact: When a polar bear cub is born, it can not see or hear. It takes approximately a month for the cub to start to see and hear
• n approximation The act of approximating; a drawing, moving, or advancing near in space, position, degree, or relation; approach; proximity.
• n approximation In mathematics and physical: A continual approach to a true result; the process by which the value of a quantity is calculated with continually increasing exactness without ever being actually ascertained
• n approximation A result so obtained; a result which is not rigorously exact, but is so near the truth as to be sufficient for a given purpose.
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Chambers's Twentieth Century Dictionary
• Interesting fact: In the United States, approximately seven billion pounds of chocolate and candy are manufactured each year
• n Approximation an approach: a result in mathematics not rigorously exact, but so near the truth as to be sufficient for a given purpose
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## Quotations

• Christian Nevell Bovee
“Example has more followers than reason. We unconsciously imitate what pleases us, and approximate to the characters we most admire.”
• Sigmund Freud
“Every normal person, in fact, is only normal on the average. His ego approximates to that of the psychotic in some part or other and to a greater or lesser extent.”

## Etymology

Webster's Revised Unabridged Dictionary
Cf. F. approximation, LL. approximatio,
Chambers's Twentieth Century Dictionary
L. approximāre, -atumad, to, proximus, nearest, superl. of prope, near.

## Usage

### In literature:

New Zealand is approximately the antipodes to France.
"Astronomy for Amateurs" by Camille Flammarion
Nevertheless, they can be approximated with enough accuracy for our purpose.
"The Pioneer Steamship Savannah: A Study for a Scale Model" by Howard I. Chapelle
ENERGINE: A powerful stimulant, effective for approximately eight hours.
"Concordance" by Ann Wilson
Their specific abilities differed, but the general level was approximately the same.
"A Matter of Honor" by Ann Wilson
It is also approximate to that assigned for the Solomon Islands.
"Celebrated Travels and Travellers" by Jules Verne
The postulates, however, were taken by the economists to represent something more than approximate statements of the fact.
"The English Utilitarians, Volume II (of 3)" by Leslie Stephen
Lines which continually approximate each other, but can never meet.
"The Sailor's Word-Book" by William Henry Smyth
We remark farther, that there are supportable approximations, and then likewise insupportable.
"Past and Present" by Thomas Carlyle
The flow is also more steady, and the volume can be in a measure approximated from general experience.
"Principles of Mining" by Herbert C. Hoover
The rendezvous point is selected with regard to the natural channels of movement approximately straight to the rear.
"Manual of Military Training" by James A. Moss
In 1911 the total value of the prizes offered in the South to the boys' corn clubs approximated fifty thousand dollars.
"The New Education" by Scott Nearing
Nightfall loomed imminent when we reached the town of Abbevilliers, a place of approximately twenty thousand inhabitants.
"Fibble, D. D." by Irvin Shrewsbury Cobb
On the Divine side all prophecy is certain, but on the human it can only be approximated.
"The Lost Ten Tribes, and 1882" by Joseph Wild
The supposition that labor and capital go thus together from one grade of land to another is only approximately accurate.
"Essentials of Economic Theory" by John Bates Clark
The area covered by the ruins is approximately 1 sq.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 2" by Various
Spines on the upper segments of the posterior cirri, arranged in three or four approximate longitudinal rows, making small brushes.
"A Monograph on the Sub-class Cirripedia (Volume 1 of 2)" by Charles Darwin
By the latter he means settlements which were occupied at approximately the time of the American invasion of 1850.
"The Aboriginal Population of the North Coast of California" by Sherburne Friend Cook
Of these only 2 or 3 contained abundant water; approximately 10 had only a small amount.
"The Aboriginal Population of Alameda and Contra Costa Counties, California" by S. F. Cook
The best estimate that can be made is that the cost of collection per packet is approximately the same in all cases.
"The Development of Rates of Postage" by A. D. Smith
After such treatment the cake should contain approximately 15 per cent.
"Soap-Making Manual" by E. G. Thomssen
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### In poetry:

No charges can approximate
The worth of sympathy with woe; -
Although I think I ought to state
He did his best to make them so.
"Baines Carew, Gentleman" by William Schwenck Gilbert
After the cessation
I might be a soul in bliss, an angel, approximating to the
Uplifted;
But that is another matter;
I am Matthew, the man,
And I am not that other angelic matter.
"St. Matthew" by D H Lawrence

### In news:

What demand there is, he said, would result in approximately 100 hours of crushing a year.
The maximum value of the services to be provided by Cubic to RailCorp (Rail Corporation New South Wales) under the contract is expected to be approximately \$65 million.
This 5-inch cuddly panda was created using a straight, medium-density alpaca approximately ¼ inch in length.
LINCOLN--If the aging workers of Nebraska's approximately 60,000 farms are going to be replaced, the schools are the best place to start.
FM 39 is closed in Madison County due to a culvert washing out from the rains we have received the past few days FM 39 is closed approximately four miles from the Grimes County Line.
The work will take approximately 10 days to complete.
Announced that it has acquired the stock of Benshaw Advanced Controls & Drives, Pittsburgh, for approximately \$102 million in cash.
Could you please tell me about Cushing's disease in a mixed breed that is approximately 10 years old.
This number, says Marketing and Consulting for Digital Broadcasting Technologies, takes the audience to approximately 2.4 million, just under a third of all Swiss households.
Under his direction, Palio's 20 well-trained kitchen staffers serve approximately 500 lunches and dinners each day.
We had just gotten a dalmatian puppy a few months prior, when we saw someone who had to give up their female dalmatian pup, of approximately the same age, due to a change in circumstance.
On June 19, Edgewater Fire-Rescue's Engine 57 was dispatched to a home on Victory Palm Drive in the Florida Shores neighborhood for an unresponsive patient at approximately 6:30 pm.
The ship had been seized approximately 600 nautical miles off the Somali coast carrying roughly \$170 million worth of Iraqi crude oil.
E-Series consume about half the water (approximately 10-20 gallons per load less) than traditional hard-mount washers and offer high-speed extract reaching 387 G-force.
I led an international organization that consisted of approximately 8,000 people.
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### In science:

In this approximation, and this is an approximation that we will use in the present paper, the problem of the moving oscillator is equivalent to the problem of the propagation of the wave packet in the electric ﬁeld ~E .
Space-Time Evolution of the Oscillator, Rapidly moving in a random media
The Gaussian approximation and square approximation to the measurement error distribution.
A Search for Gamma-Ray Bursts and Pulsars, and the Application of Kalman Filters to Gamma-Ray Reconstruction
We have demonstrated the effectiveness of our method by calculating a high-quality semiclassical spectrum for the hydrogen atom in an electric ﬁeld in a spectral region where the semiclassical approximation without uniform approximations would be completely useless due to the abundance of bifurcations.
Semiclassical quantization with bifurcating orbits
Johnson, Computers and Intractability, (Freeman, San Francisco 1979). Please note that “approximation” is not used in the sense of a polynomial-time approximation scheme, which guarantees to approximate the optimal solution within some given error for arbitrary samples.
Dynamics of heuristic optimization algorithms on random graphs
The quality of the approximation increases with growing initial c0 , supporting thus our conjecture that the asymptotic behaviour is correctly described by the approximation.
Dynamics of heuristic optimization algorithms on random graphs
Using an Approximate Oracle If the subroutine for computing minx∈P Pj yj fj (x) returns only an approximate minimizer x, our algorithms still work well.
Randomized Rounding without Solving the Linear Program
The appearance of the ratio of the lapse N may be somewhat surprising, but the quasi-equilibrium approximation (and the existence of the approximate Killing vector ∂/∂ t + Ω∂/∂φ) eliminate the arbitrary nature of the lapse.
Variational Principles in General Relativity
This is a very powerful statement and indicates a rudimentary method to improve our approximate solution vh to Eq. (4.1): Assuming some approximate solution vh has been found by some means, calculate the residual rh .
Variational Principles in General Relativity
Calculate the residual due to the approximate solution using the nonlinear residual equation, Eq. (4.17). • Restrict the residual from level h to level 2h via r2h = I 2h h rh , and restrict the updated approximate solution from level h to level 2h via v 2h = I 2h h uh .
Variational Principles in General Relativity
Note the updated ﬁne grid approximation becomes the initial coarse grid approximation.
Variational Principles in General Relativity
On reaching the smallest adaptive level the residual error, a measure of how well the approximate solution is solving the ﬁnite difference equation, and the truncation error, a measure of how much the approximate solution is changing from one iteration to the next, may be calculated.
Variational Principles in General Relativity
Such an approximation allows density to become negative (if extremely low probability), and since those very regions of low trap density govern to dynamics, the importance of those unphysical conﬁgurations is enhanc ed which completely messes any analysis based on the Gaussian noise approximation.
Trapping of a random walk by diffusing traps
Non-trivial left ω -approximations do exist for modules in R, non-trivial right ω -approximations for modules in Q.
Infinite dimensional representations of canonical algebras
There is another substantial difference: let us compare the possible minimal left ω -approximations Mω and minimal right ω -approximations M ω of ﬁnite dimensional modules M .
Infinite dimensional representations of canonical algebras
However, if the replacement is done with some approximate form of the auxiliary ﬁelds distribution function, the real free-energy will be the one calculated using the approximate ﬁelds plus an excess term at every step of the graph deletion process.
Replica bounds for optimization problems and diluted spin systems
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