We provide bounds for the product of the lengths of distinguished shortest paths in a finite network induced by a triangulation of a topological planar quadrilateral.

A sinusoidal grating can be viewed as a series of light and dark bars. Here we measure the contrast discrimination thresholds for light and dark bars individually, and find that the contrast discrimination thresholds for the whole sinusoid can be explained as ideal summation of the light and dark bar thresholds. We propose a model for light bar, dark bar, and sinusoidal contrast discrimination ...

We show that three π/6 vertex floodlights suffice to illuminate any triangle, and we prove that any quadrilateral can be illuminated by three π/4 vertex floodlights.

This research aims to diagnose students' difficulties in solving the TIMSS model mathematics test. used quantitative descriptive method. The subjects of study is eighth-grade students junior high school Cirebon, Indonesia. Data collection was carried out through a simple random sampling technique including 676 from 13 public and private schools. instrument modelmathematics test form multiple-ch...

Four points ordered in the positive order on unit circle determine vertices of a quadrilateral, which is considered either as euclidean or hyperbolic quadrilateral depending whether lines connecting are lines. In case lines, this type quadrilaterals called ideal quadrilaterals. Our main result gives counterpart an earlier distances between opposite sides The proof based computations involving g...