Question 156
Let $\mathcal{C}$ be a circle of radius $1$, and let $T$ be a real number. We say that a set of triangles is $T$-merarious if it satisfies the following three conditions:
$\triangleright$ the vertices of each triangle belong to $\mathcal{C}$;
$\triangleright$ the triangles have pairwise disjoint interiors (but two triangles may share a side or a vertex);
$\triangleright$ each triangle has perimeter strictly greater than $\mathbf{T}$.
Find all real numbers $\mathbf{T}$ such that, for every integer $\mathrm{n} \geqslant 1$, there exists a $T$-merarious set containing exactly $n$ triangles.
$\triangleright$ the vertices of each triangle belong to $\mathcal{C}$;
$\triangleright$ the triangles have pairwise disjoint interiors (but two triangles may share a side or a vertex);
$\triangleright$ each triangle has perimeter strictly greater than $\mathbf{T}$.
Find all real numbers $\mathbf{T}$ such that, for every integer $\mathrm{n} \geqslant 1$, there exists a $T$-merarious set containing exactly $n$ triangles.