4 problems

Let a Jordan curve be a simple closed curve $\gamma\subset\mathbb{R}^2$. An isosceles trapezoid is a quadrilateral whose vertices are the intersection set of two parallel lines and…

Let $\gamma_1,\gamma_2\colon\mathbb{R}\to\mathbb{C}$ be continuous disjoint periodic embeddings of the real line into the plane. A quadrilateral $Q$ admits an inscription in any pa…

Let $\gamma_1,\gamma_2\colon\mathbb{R}\to\mathbb{C}$ be continuous embeddings satisfying … for every $t$ and $i=1,2$, with disjoint images. Tao's square inscription conjecture. The…

Square-like quadrilateral conjecture. There is a square-like quadrilateral inscribed in any embedding of $S^1$ in $\mathbb{R}^n$.