We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an efficient scheme for rendering triangulated manifolds by graphics hardware. We also show that the Hamiltonian Cycle problem is NP-Complete for planar subcubic graphs of arbitrarily high girth. As a by-product we prove that there exist tri-Hamiltonian planar subcubic graphs of arbitrarily high gir...

Experimental study of natural convection heat transfer inside smooth and rough surfaces of vertical and inclined equilateral triangular channels of different inclination angles with a uniformly heated surface are performed. The inclination angle is changed from 15o to 90o. Smooth and rough surface of average roughness (0.02mm) are used and their effect on the heat transfer characteristics are s...

Abstract In this paper, we analyze the physical puzzle IcoSoKu, a game about placing some given triangular tiles on faces of an icosahedron in order to fill capacities its vertices, and propose generalization called 3coSoKu, admitting arbitrary playing field with faces, set tiles. First, prove strong NP-completeness even when is convex polyhedron equilateral triangles as faces. Second, encode 3...

Among other CubeSat subsystems, Antenna is one of the most important components as its design determines all telecommunication subsystems’ performances. This paper presents a coplanar wave-guide (CPW)-fed equilateral triangular slot antenna constructed and analyzed for communications at S-band. The proposed alone high gain ultra-wide band while radiation pattern bidirectional an unlicensed freq...

This paper describes the construction, properties and potential applications of a cartographic projection recently developed by the author, called the Zenithial Orthotriangular (ZOT) projection of an Octahedron. ZOT maps a planet to a plane by modelling it as an octahedron (a regular solid having 8 equilateral triangular facets), which is then unfolded and stretched to fit within a square. As d...

Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson’s equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here the literature is unified and extended by identifying 17 physical analogies for unidi...