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The plane determined by the points x_1, x_2, and x_3 and the line passing through the points x_4 and x_5 intersect in a point which can be determined by solving the four ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

Tarski's theorem says that the first-order theory of reals with +, *, =, and > allows quantifier elimination. Algorithmic quantifier elimination implies decidability assuming ...

The Thomson problem is to determine the stable equilibrium positions of n classical electrons constrained to move on the surface of a sphere and repelling each other by an ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...