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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 ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...

A plane parallel to two (or more) skew lines, also called a director plane. The orientation of a director is fixed, but it is specified uniquely only if a point lying on it ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

A requirement necessary for a given statement or theorem to hold. Also called a criterion.

Arrow's paradox, also called Arrow's impossibility theorem or the general possibility theorem, states that perfect democratic voting is impossible, not just in practice but ...

The rule (F,F=>G)/G, where => means "implies," which is the sole rule of inference in propositional calculus. This rule states that if each of F and F=>G is either an axiom ...

The point that inversion of a curve is performed with respect to.