The Pentagon's Military Analyst Program

Fullerenes with distant pentagons

For each d > 0, we find all the smallest fullerenes for which the least distance between two pentagons is d. We also show that for each d there is an hd such that fullerenes with pentagons at least distance d apart and any number of hexagons greater than or equal to hd exist. We also determine the number of fullerenes where the minimum distance between any two pentagons is at least d, for 1 ≤ d...

Acute Triangulations of Pentagons

An acute triangulation is a triangulation whose triangles have all their angles less than π 2 . In this paper we prove that i) every planar pentagon can be triangulated into at most 54 acute triangles, and ii) every double pentagon can be triangulated into at most 76 acute triangles.

The Grunert Point of Pentagons

1. Introduction. "Remarkable points" of triangles –– for example, the centroid, the circumcenter and others –– have been studied in detail; in fact, the recent book [3] by Clark Kimberling contains information on 400 such "centers". Although one can expect that in case of quadrangles there should be an even larger number of "remarkable points" –– only few have been discussed in the literature. ...

The Behavior Analyst Today

The Behavior Analyst Today