7 problems

Polar Harmonic-family conjecture. The sum of half-angle tangents is conserved for the polar image of the Harmonic family, for all $N>3$.

Stationary-orthocenter classification conjecture. A Poncelet triangle family maintains $X_4$ stationary only if the conics are configured as focal-$X_4$, MacBeath, or Dual.

Let $\mathcal{T}_{\circ}$ be the Poncelet family whose circumcircle is constrained by the circular caustic, and let $\Gamma$ denote the line associated with the circumcircle-incent…

Let $\mathcal{T}$ be the family of Poncelet triangles, and let $\mathcal{E}_c$ be the inner Poncelet caustic. Consider the envelope of the circumcircle as the triangles range over…

Let $\mathcal{E}$ be the outer ellipse and let $\mathcal{E}_c$ be the inner Poncelet caustic. Consider the two envelopes associated with the Poncelet family: the envelope of the ci…

Let $T$ be a reference triangle, and let $T'$ be its $X_{55}$-reflection triangle. The six vertices of the P-hyperbolas of $T'$ passing through $X_{55}$ of $T$ are the six points a…

The theory of conic sections and the practical observations of sundials are the relevant mathematical objects. De la Hire's conjecture. The theory of conic sections originated in t…