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A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...

Given a point P, the pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the side lines. The pedal triangle of a triangle ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

Let (X,tau) be a topological space, and let p in X. Then the arc component of p is union {A subset= X:A is an arc and p in A}.