# Approximations Sentence Examples

The Remez algorithm is then used to compute the new

**approximations**.When a first approximation has been obtained in this way, further

**approximations**can be obtained in various ways.As far as the order to which he carried the

**approximations**- which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.If we use c 1 to represent the chord of the whole arc, c 2 the chord of half the arc, and c 4 the chord of one quarter of the arc, then corresponding to (i) and (iii) of § 70 or § 79 we have a (8c 2 - c i) and4 5 (256c 4 - 40c2+ci) as

**approximations**to the length of the arc. The first of these is Huygens's rule.Such theories, as we have noticed, are extremely likely to be only

**approximations**in ancient times, even if recognized then; and our data are quite inadequate for clearing the subject.By testing the beam with the scale-pans attached and equal weights in the pans, and noting carefully the position which it takes up; and then interchanging the scale-pans, &c., and again noting the position which the beam takes up, a correct inference can be drawn as to the causes of error; and if after slightly altering or adjusting the knife-edges and scale-pans in the direction indicated by the experiment, the operation is repeated, any required degree of accuracy may be ob - tained by successive

**approximations**.In actual practice, however, decimals only represent

**approximations**, and the process has to be modified (§ 111).In the Principia Newton made several investigations to determine the effects of these actions; but the geometrical method which he employed could lead only to rude

**approximations**.In theory these successive

**approximations**may be carried as far as we please, but in practice the labour of executing each approximation is so great that we are obliged to stop when the solution is so near the truth that the outstanding error is less than that of the best observations.While linear methods have proven invaluable over many years in generating first-order

**approximations**, they are severely limited in both qualitative and quantitative predictions.AdvertisementThe

**approximations**behind the quadratic residue diffuser 's design have been tested.The approach assumes a self-similar fractal - this result suggests considerable

**approximations**are involved in the application of box counting to discrete FBM.Hence

**approximations**of the eigenfrequencies for the longitudinal and torsional vibrations can be found immediately.Rough

**approximations**must always precede accurate measurements; and these returns, while often inaccurate, are better than nothing, and probably improve with each decade.Calculations in QED are carried out via " Feynman diagrams " which are successive

**approximations**to QED.AdvertisementCollecting sample boards that contain paint chips, fabric swatches, and pictures of furniture can help you integrate actual colors, rather than the rough

**approximations**that some design tools offer.Quotes are just

**approximations**of what your health care package will cost.Note, though, that calculators are only

**approximations**of reality; your actual retirement pay will be calculated based on personal and systemic factors in force at the time of your retirement.While

**approximations**of the pronunciation of these French phrases are given, it is impossible to provide a perfect pronunciation key using English sounds to guide French pronunciation.It must not be forgotten, too, that a very moderate increase of dimensions may carry the particles beyond the reach of our

**approximations**.AdvertisementIt is, for instance, practically impossible to obtain reliable evidence as to the regularity of employment in any industry in the 17th century, and the best

**approximations**and devices we can invent are very poor substitutes for what we really want.Amongst insects with imperfect metamorphosis the nearest

**approximations**to the true pupa of the Holometabola are to be found in the subimago a From Chittenden, Bull.The problem of finding a radius vector satisfying this condition is one which can be solved only by successive

**approximations**, or tentatively.A remarkable feature is the bare statement of a number of very close

**approximations**to the square roots of numbers which are not complete squares.Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting

**approximations**to the values of trigonometrical ratios.AdvertisementFor the exact determination of the last element the census affords no precise data, but affords material for various

**approximations**, based either upon the elimination of the probable progeny of immigrants since 1790; on the known increase of the whites of the South, where the foreign element has always been relatively insignificant; on the percentage of natives having native grandfathers in Massachusetts in 1905; or upon the assumed continuance through the 19th century of the rate of native growth (one-third decennially) known to have prevailed down at least to 1820.The following table gives the values of this constant and several expressions involving it Useful fractional

**approximations**are 22/7 and 355/113.Pappus gives several solutions of this problem, including a method of making successive

**approximations**to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.He holds that space, time, matter, motion, force, are all full of the insoluble contradictions supposed by Spencer; and that all our beliefs, in Nature and in God, stand on the same footing of

**approximations**.In these new fields he displayed the powers so conspicuous in his scientific inquiries, and he was now to introduce and establish scientific accuracy where previously there had been merely practical

**approximations**.He uses them for

**approximations**.Below is a chart which gives

**approximations**of the cost of one of these gemstones per carat, based on various colors.