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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. ...

The polyhedron compound of the icosahedron (U_(22)) and the great dodecahedron (U_(35)), sometimes known as the small cid. Four faces meet at each edge of the small complex ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...