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The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point D and a circle is ...

A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

The orthojoin of a point X=l:m:n is defined as the orthopole of the corresponding trilinear line lalpha+mbeta+ngamma. In other words, the orthojoin of Kimberling center X_i ...

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 ...

Consider a reference triangle DeltaABC and any given point P. The perpendiculars to AP, BP and CP respectively meet BC, AC and AB in three collinear points defining line l. ...

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...