Inherited conics in Hall planes

Elementary Constructions for Conics in Hyperbolic and Elliptic Planes

In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective affinities (de la Hire’s construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the...

Codes from Hall planes of even order

We show that the binary code C of the projective Hall plane Hq2 of even order q where q = 2, for t ≥ 2 has words of weight 2q in its hull that are not the difference of the incidence vectors of two lines of Hq2 ; together with an earlier result for the dual Hall planes of even order, this shows that for all t ≥ 2 the Hall plane and its dual are not tame. We also deduce that dim(C) > 3+1, the di...

A Characterization of the Hall Planes

In this article, the Hall planes of even order q2 arc characterized as translation planes of even order q2 admitting a Baer group of order q and at least q+l nontrivial elations.

Discrete Conics

In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the discrete negative pedal construction and an action of a group acting on a focus-sharing pencil of conics.

Liquids with conics