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In this note, we prove the existence of the analogous points of the Gergonne and Nagel points and their adjoint points for the case of a non-degenerate hyperbolic triangle and find their barycentric coordinates with respect to the given triangle. Unlike their classical counterparts, the hyperbolic points we construct may as well be ideal or ultra-ideal, depending on the triangle. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a new characterization of Möbius transformations by use of hyperbolic regular polygons. [ABSTRACT FROM AUTHOR]

In this note, we present a proof of the hyperbolic a Smarandache's pedal polygon theorem in the Poincaré disc model of hyperbolic geometry. [ABSTRACT FROM AUTHOR]

In this study, we present (i) a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, (ii) and a proof for the transversal theorem for triangles, and (iii) the Menelaus's theorem for n-gons. [ABSTRACT FROM AUTHOR]

A rigorous test is presented of the application of sediment trend models to an intertidal beach environment characterized by bar morphology. Sediment samples were collected during low tide from a regular grid and their sediment fall velocity distributions, obtained using a settling tube, were analysed using moment analysis. The net sediment transport direction determined from beach surveys, hydrodynamic measurements, wave ripple observations and sediment transport modelling was compared with predictions by sediment trend models based on the spatial distribution of sediment parameters. It was found that the sediment transport pathways and patterns of sedimentation predicted using sediment trend models were at odds with field observations, and varied significantly depending on whether surface or sub-surface sediment samples were used. The sediment trend models are thought to fail because, in energetic and morphologically variable beach environments, spatial patterns in sediment characteristics are mainly attributed to the presence of different hydrodynamic regions and associated morphology, rather than sediment pathways. The use of sediment trend models cannot replace the collection of morphological, hydrodynamic and sediment transport data in the field to define relationships between flows, forms and sedimentation patterns on a dynamic intertidal beach. [ABSTRACT FROM AUTHOR]