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A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

Let I be the incenter of a triangle DeltaABC and U, V, and W be the intersections of the segments IA, IB, IC with the incircle. Also let the centroid G lie inside the ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

The golden gnomon is the obtuse isosceles triangle whose ratio of side to base lengths is given by 1/phi=phi-1, where phi is the golden ratio. Such a triangle has angles of ...

A golden rhombus is a rhombus whose diagonals are in the ratio p/q=phi, where phi is the golden ratio. The faces of the acute golden rhombohedron, Bilinski dodecahedron, ...

Successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the golden spiral. ...