Walker's System of Geometrical Conics

conics in mathematical textbooks of contemporary educational system of iran

conics or the science of conic sections is one of the highest theoretical topics of geometry in classical antiquity and the middle ages. it was also studied for its practical applications. in this paper, we first present a short history of conics in antiquity and the islamic civilization, then we show how this discipline was introduced in persian textbooks in the qajar period and a little after...

Lattice paths: vicious walkers and friendly walkers

In an earlier paper [4] the problem of vicious random walkers on a d-dimensional directed lattice was considered. \Vicious walkers" describes the situation in which two or more walkers arriving at the same lattice site annihilate one another. Accordingly, the only allowed con gurations are those in which contacts are forbidden. Alternatively expressed as a static rather than dynamic problem, vi...

The Conics of Ludwig Kiepert:

If a visitor from Mars desired to leam the geometry of the triangle but could stay in the earth' s relatively dense atmosphere only long enough for a single lesson, earthling mathematicians would, no doubt, be hard-pressed to meet this request. In this paper, we believe that we have an optimum solution to the problem. The Kiepert conics, though seemingly unknown today, constitute a significant ...

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