Search Results for ""

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

Let a line in three dimensions be specified by two points x_1=(x_1,y_1,z_1) and x_2=(x_2,y_2,z_2) lying on it, so a vector along the line is given by v=[x_1+(x_2-x_1)t; ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...