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There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

For triangles in the plane, AD·BE·CF=BD·CE·AF. (1) For spherical triangles, sinAD·sinBE·sinCF=sinBD·sinCE·sinAF. (2) This can be generalized to n-gons P=[V_1,...,V_n], where ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

A triple of three arbitrary vectors with common vertex (Altshiller-Court 1979), often called a trihedral angle since it determines three planes. The vectors are often taken ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...