I want to maximize the number of similar triangles with vertices from three fixed sets, one vertex from each set. For example, if you fix two points $X$, $Y$ (i.e. two sets with only one member), then ...
Question : Is the following true? "Letting $K$ be a convex bounded closed set on a plane, then there exists a triangle $M$, which includes $K$, such that $|M|\le 2|K|$. Here, $|M|,|K|$ is the area of ...
The lines which bisect the area of a triangle form an envelope as shown in this picture It is not difficult to show that the ratio of the area of the red deltoid to the area of the triangle is ...
I've been trying to find, without much success, 4 triangles whose corresponding sides are congruent that cannot be folded into a tetrahedron. Anyone has any clue how to approach this problem?