A pentagon in the plane with fixed side-lengths has a two-dimensional shape space. Considering the pentagon as a mechanical system with point masses at the corners we answer the question of how much the pentagon can rotate with zero angular momentum. We show that the shape space of the equilateral pentagon has genus 4 and find a fundamental region by discrete symmetry reduction with respect to ...

An engineering lesson derived from the tragedies of the 9/11 Pentagon crash and Hurricane Katrina is the importance of resiliency in designing for multiple hazards. In the case of the Pentagon, the energy-absorbing capacity, redundancy, and continuity of the structural frame reduced the consequences of the unanticipated action. In Katrina, the hurricane protection system breached in forty-six p...

This article examines the relationship between warfare and the media, arguing that both terrorists and conventional warfare planners in the Pentagon factor communications and public relations into their planning. In this regard, the article sketches out how the Pentagon developed a new genre of ‘public relations-ized’ warfare – warfare planned, not only as a military exercise, but as a televisu...

Carbon, the basic building block of our universe, enjoys a vast number of allotropic structures. Owing to its bonding characteristic, most carbon allotropes possess the motif of hexagonal rings. Here, with first-principles calculations, we discover a new metastable three-dimensional carbon allotrope entirely composed of pentagon rings. The unique structure of this Pentagon Carbon leads to extra...

Abstract The five circles in the classical Pentagon theorem of Miquel are given as circumcircles certain triangles pentagon. If one chooses instead other triangles, gets a different configuration circles. This resulting carries three families concyclic quadruples points. Together with this gives total 20 radical axes each two these twenty all concurrent.

It is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180 o or it is the unique equilateral convex pentagon with Although the area of mathematical tilings has been of interest for a long time there is still much to be discovered. We do not even know which convex polygons tile the plane. Furthermore, for those polygons which do tile, new tilin...

We show that solutions of Pentagon equations lead to solutions of the Tetrahedron equation. The result is obtained in the spectral parameter dependent case. URA 1436 ENSLAPP du CNRS, associée à l’Ecole Normale Supérieure de Lyon et au Laboratoire d’Annecy de Physique des Particules. email: [email protected] Ref. ENSLAPP xxx/93 November 1993

We discovered the new tiling patterns each of which is composed of a single kind of convex pentagon. Moreover, we propose a new concept of classification method of the tessellating convex pentagons, which is the only unsolved case among the corresponding tessellating convex polygon problems.