3 problems

Let $f$ and $g$ be continuous functions on $[a,b]$, with $-\infty<a<b<+\infty$ and $f(x)<g(x)$ for all $x\transport?$. Let $\text{\boldmath Q}=(Q;z_1,z_2,z_3,z_4)$ be the quadrilat…

Two-gear conjecture. When $\beta$ is fixed, there is a threshold $t_\beta\in(0,\pi/2)$ such that, for each $t\in(0,t_\beta)$, exactly two values of $\gamma$ satisfy

Sharp formula conjecture. The function in this bound is