5 problems

A bicentric pedal polygon is obtained from a bicentric polygon by taking its pedal polygon with respect to a limiting point, denoted by $\ell_1$ or $\ell_2$. Cosine-sum invariance…

A focus-inversive polygon is obtained from an $N$-periodic billiard polygon by the focus-inversive construction described in the paper. Its perimeter is denoted by $L^\dagger$. Per…

Excentral $X_3$-inconic conjecture. The ratio $\mu'_3/\mu_3$ is invariant over all 3-periodics and is given by

Moses' pencil conjecture. Over the family of 3-periodics, all circumellipses in Moses' pencil conserve the ratio of their axes.

Let $N$ be the period of an orbit in an elliptic billiard, let $\theta_1,\theta_2,\ldots,\theta_N$ be its orbit angles, let $r$ and $R$ denote the inradius and circumradius of the…