The Guardian – Alex Bellos
“Today’s puzzle is simple and spectacular. It asks you to construct a triangle whose existence seems to defy reason. Show that there is a triangle, the sum of whose three heights is less than 1mm, that has an area greater than the surface of the Earth (510m km2). Instinctively, one feels that such a triangle is impossible. How can something that is so arbitrarily tiny be so arbitrarily big? Yet it is possible to describe such a triangle using the tools of elementary geometry.” (more)