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Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection array {12,11,10,7;1,2,5,12}. It is however not ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...