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Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

The initial side of an angle theta drawn in angle standard position is the side lying on the positive x-axis. In general, viewing an angle as the amount of rotation about the ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

Given an original triangle (thick line), find the medial triangle (outer thin line) and its incircle. Take the pedal triangle (inner thin line) of the medial triangle with ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

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 ...

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

A function y=f(x) has critical points at all points x_0 where f^'(x_0)=0 or f(x) is not differentiable. A function z=f(x,y) has critical points where the gradient del f=0 or ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.