Weak Conics Hub

This chart shows the logical organization of weak points lines and conics that builds from Io, the original incenter. It includes every weak conic abut whicgh there has been discussion that I could find.

Weak conics are can be considered to originate from the incenter and have multiple versions. The links below show all versions. These conics are weakened versions of the strong ones.

Each circle represents a point, each box a line, and each oval a conic. The connecing lines represent affine invariant operations: t is the isotomic conjugate, m and d are the medial and dilated (antimedial) operations, and ~ means the dual.

The isotomic conjugate takes points to points and lines to conics. The dual operation takes points to lines, lines to points, and changes a circumconic to an inconic (and vice-versa). The dual of a point on a circumconic is a tangent line to an inconic (and vice-versa).

Click on the name of a conic to see pictures and information about it. Not all are implemented yet. Gray text indicates conics that are in the logical system but seem not very important in that there has been little discussion of them.

This organizational structure is a universal structure, just choose a different starting point. The centroid, line at infinity and the Steiner ellipses are in each schema.