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The converse of Pascal's theorem, which states that if the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the ...

In general, a cross is a figure formed by two intersecting line segments. In linear algebra, a cross is defined as a set of n mutually perpendicular pairs of vectors of equal ...

A set partition of the rational numbers into two nonempty subsets S_1 and S_2 such that all members of S_1 are less than those of S_2 and such that S_1 has no greatest ...

The dihedral angle is the angle theta between two planes. The dihedral angle between the planes a_1x+b_1y+c_1z+d_1 = 0 (1) a_2x+b_2y+c_2z+d_2 = 0 (2) which have normal ...

A discriminant is a quantity (usually invariant under certain classes of transformations) which characterizes certain properties of a quantity's roots. The concept of the ...

A surface of revolution which is generalization of the ring torus. It is produced by rotating an ellipse having horizontal semi-axis a, vertical semi-axis b, embedded in the ...

The Fibonacci Q-matrix is the matrix defined by Q=[F_2 F_1; F_1 F_0]=[1 1; 1 0], (1) where F_n is a Fibonacci number. Then Q^n=[F_(n+1) F_n; F_n F_(n-1)] (2) (Honsberger ...