Sentence examples for a useful approximation from inspiring English sources

Even using a limited number of contours provides a useful approximation to the 3D face surface.

The C + NVC model with the incorporation of Wu et al. (2009) outputs was adapted for use in this paper, it was shown to give a useful approximation of the difference between scenarios, and could be further utilised with specific wildfire management data (i.e. pre-suppression efforts–such as prescribed burning) if and where available.

It may be viewed as a refinement of the arithmetic mean: the latter has been a useful approximation in economic analysis [5,6], whilst the new mean should find use both in flowsheeting programs and in rapid rating calculations a in the example above.

This theory provides a useful approximation of the historical changes that have taken place in populations in many different regions of the world.

The body mass index is a useful approximation of body fat, but it can be misleading for muscular athletic individuals, like President Bush, who would be considered overweight, as the article notes.

Many would defend utility theory (as well as other aspects of their standard model of behaviour) as a useful approximation, pointing out that exceptions to approximations can always be found.

Although Jakob Bernoulli did not know Chebyshev's inequality, the inequality he derived was also imprecise, and, perhaps because of his disappointment in not having a quantitatively useful approximation, he did not publish the result during his lifetime.

Simulations show that it is a rather useful approximation.

A very useful approximation to this relation is established through numerical experiments which is exact for all practical purposes.

This expression provides what we think is a potentially useful approximation for the group velocity times wave energy (the solid black lines) for all types of equatorial waves, as we show in the "Methods/Experimental" section.

The Taylor series of ln z provides a particularly useful approximation to ln(1+z) when z is small, |z| < 1, since then : \ln (1+z) = z - \frac{z^2}{2} +\frac{z^3}{3}\approx\approx z.