We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call " geodetic ". We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecom...

Geodetic sets in graphs are briefly surveyed. After an overview of earlier results, we concentrate on recent studies of the geodetic number and related invariants in graphs. Geodetic sets in Cartesian products of graphs and in median graphs are considered in more detail. Algorithmic issues and relations with several other concepts, arising from various convex and interval structures in graphs, ...

The geodetic problem was introduced by Harary et al. [17]. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic problem. The problem is solved for complete Apollonian networks. It is also proved that in general the strong geodetic problem is NP-complete.

An undirected graph G = (V;E) is said to be geodetic, if between any pair of vertices x; y 2 V there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are de ned as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k{geodetic graphs are studied.

A set of vertices S in a graph is called geodetic if every vertex of this graph lies on some shortest path between two vertices from S. In this paper, minimum geodetic sets in median graphs are studied with respect to the operation of peripheral expansion. Along the way geodetic sets of median prisms are considered and median graphs that possess a geodetic set of size two are characterized. © 2...

Standard Molodensky is a recognised method of transforming coordinates between geodetic datums. Although less accurate than some other methods, it has the merit being direct. That to say can be applied coordinates, without involving Cartesian that give rise difficulties in computing latitude. This paper considers use when at least one datums 2D+1D nature, meaning horizontal and vertical positio...

Cellular vehicle-to-everything(C-V2X) technology can protect vulnerable road users(VRUs) in traffic accidents. Smartphones are the most common portable devices for VRUs, but they do not support direct communication between vehicles and pedestrians. To address this problem, we propose a vehicle-to-pedestrian collision warning system that includes phone case designed smartphone. It allows VRUs to...

Measurements in the coastal zone are carried out using various methods, including Global Navigation Satellite Systems (GNSS), hydroacoustic and optoelectronic methods. Therefore, it is necessary to develop coordinate transformation models that will enable conversion of data from land marine parts one system. The article presents selected issues related integration geodetic hydrographic data. ai...

Abstract In this study, positioning quality is tested with the use of low-cost in-house developed receivers. The analyzes consider practical devices in surveying works. network solution, accuracy GNSS based on receivers can be characterized by repeatability baseline length 1 and 6 mm 24 h 10 min observation sessions, respectively. field experiment 4 3 allowed for establishing a precise geodetic...