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A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

A transformation of the plane which transforms collinear points into collinear points. A projective collineation transforms every one-dimensional form projectively, and a ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

An entire Cremona transformation is a birational transformation of the plane. Cremona transformations are maps of the form x_(i+1) = f(x_i,y_i) (1) y_(i+1) = g(x_i,y_i), (2) ...

A plane parallel to two (or more) skew lines, also called a director plane. The orientation of a director is fixed, but it is specified uniquely only if a point lying on it ...

A pair of conics obtained by expanding an equation in Monge's form z=F(x,y) in a Maclaurin series z = z(0,0)+z_1x+z_2y+1/2(z_(11)x^2+2z_(12)xy+z_(22)y^2)+... (1) = ...

A perspective collineation in which the center and axis are incident.

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

A point-to-line and line-to-point transformation which transforms points A into lines a^' and lines b into points B^' such that a^' passes through B^' iff A^' lies on b.