Search Results for ""

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

A homogeneous ideal I in a graded ring R= direct sum A_i is an ideal generated by a set of homogeneous elements, i.e., each one is contained in only one of the A_i. For ...

The intersection of two sets A and B is the set of elements common to A and B. This is written A intersection B, and is pronounced "A intersection B" or "A cap B." The ...

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

Two planes that do not intersect are said to be parallel. Two planes specified in Hessian normal form are parallel iff |n_1^^·n_2^^|=1 or n_1^^xn_2^^=0 (Gellert et al. 1989, ...

The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

A conical surface modeled after the shape of a seashell. One parameterization (left figure) is given by x = 2[1-e^(u/(6pi))]cosucos^2(1/2v) (1) y = ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...