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Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

A sphere with a single cross-cap. This term is more appropriate in purely topological applications than the more common term real projective plane, which implies the presence ...

A cylindric section is the intersection of a plane with a right circular cylinder. It is a circle (if the plane is at a right angle to the axis), an ellipse, or, if the plane ...

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

A n-dipyramidal graph is the skeleton of an n-sided dipyramid. It is isomorphic to the (m,2)-cone graph C_m+K^__2, where C_m is a cycle graph, K^__2 is the empty graph on 2 ...

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...