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Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

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 orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

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 ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

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 ...

The pentagonal antiprism is the antiprism having a regular pentagon for the top and bottom bases. It is also the uniform polyhedron with Maeder index 77 (Maeder 1997) and ...

The pentagonal dipyramid is one of the convex deltahedra, and Johnson solid J_(13). It is also the dual polyhedron of the pentagonal prism U_(76) and is an isohedron. It is ...

The pentagonal prism is a prism having two pentagonal bases and five rectangular sides. It is a heptahedron. The regular right pentagonal prism is uniform polyhedron U_(76). ...