|WikiProject Mathematics||(Rated B-class, Low-importance)|
|A fact from Pseudotriangle appeared on Wikipedia's Main Page in the Did you know? column on 18 April 2007. The text of the entry was as follows: "Did you know Wikipedia:Recent additions/2007/April.|
These triangles use concave sets. Something doesn't seem right. Alphachimera 01:05, 18 April 2007 (UTC)
The section "Pseudotriangles" says:
- The convex hull of any pseudotriangle is a triangle. Each of the three convex vertices is connected by a boundary curve that either lies within the triangle or coincides with one of its edges.
I can't tell what this last sentence is intended to mean. If a "boundary curve" is a path along the boundary of the pseudotriangle, then it should refer to a connecting curve that is entirely on one or more curves connecting vertices, which in the case of a polygon just lies on a sequence of one or more edges. But this would be a vacuous statement. The part about "lies within the triangle" (written so as to contrast with being on an edge) is also vacuous since by definition the pseudotriangle is simply connected.
- It is not vacuous. If you choose three random vertices of a convex polygon, the boundary curves between them all lie outside the polygon. If you choose the three convex vertices of a pseudotriangle, the boundary curves between them all lie inside the polygon. Note that a sequence of edges and vertices is an example of a curve; there is nothing in the definition of curves that prevents them from passing through vertices. (The word "smooth" is not used here.) —David Eppstein (talk) 20:21, 28 October 2015 (UTC)