Incircular nets and confocal conics

Chromogeometry and relativistic conics

If Q1 = Q(A2,A3), Q2 = Q(A1,A3) and Q3 = Q(A1,A2) are the quadrances of a triangle A1A2A3, then Pythagoras’ theorem and its converse can together be stated as: A1A3 is perpendicular to A2A3 precisely when Q1 + Q2 = Q3. Figure 1 shows an example where Q1 = 5, Q2 = 20 and Q3 = 25. As indicated for the large square, these areas may also be calculated by subdivision and (translational) rearrangemen...

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

NETS AND SEPARATED S-POSETS

Nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. In this work we introduce this concept in an $S$-poset, aposet with an action of a posemigroup $S$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $S$-net. Using $S$-nets and itsconvergency we...

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 ...