Sentence examples for locus of points from inspiring English sources

In the problem of Apollonius, for example, one sought to find the locus of points whose distances from a collection of fixed lines satisfied a given relation.

On this design space, enveloped by various constraints, various equi-parameter curves are drawn depicting locus of points on which the chosen parameter has a constant value.

Another definition of an ellipse is that it is the locus of points for which the sum of their distances from two fixed points (the foci) is constant.

A lemniscate describes "a polar curve whose most common form is the locus of points the product of whose distances from two fixed points (called the foci) a distance 2a away is the constant a^2".

Complex-impedance-plane plots are very popular because the shape of the locus of points yields insight into possible mechanisms or governing phenomena.

To derive the locus of points and the slope of the second isocline, start by rewriting expression (22) as: tau = - U^{prime}_{R}(cdot) (27).

To describe the more complicated curves produced by his instruments or defined as the loci of points satisfying involved criteria, Descartes had to include cubes and higher powers of the variables.

In this study by Bennett et al,the 3D loci of points on the acetabular component over which the femoral component moved, clearly demonstrated that the wear path extended over the edge of the acetabular component during level walking.

The region of stability is determined directly from the size of the system's injectivity radius and, for a restricted set of control problems, the system's locus of cut points about a desired reference point.

The locus of all points hit by this iteration is the attractor of the function.

Starting from classical Heyman's solution, different recently-found solutions based on the true line of thrust (locus of pressure points) are first independently re-derived.