Related papers: Problems and Exercises of Geodesy
Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the matrix Schr\"odinger equation, is…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems…
This is a survey paper on the theory of scattered spaces in Galois geometry and its applications.
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
Hilbert's fourth problem asks for the construction and the study of metrics on subsets of projective space for which the projective line segments are geodesics. Several solutions of the problem were given so far, depending on more precise…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
The method of geodesic expansions is systematically explained. Based on the Haar measures of the group of geodesic expansions the semiclassical sum over immersed manifolds is constructed. Gauge fixing is performed via the Faddeev Popov…
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
This work discusses an approach to solving geometric construction problems in which the given figure is included in a set ordered by construction steps. The flow of information is carried through the chain, allowing the original problem to…
With the aid of concrete examples, we consider the question of whether, in the presence of conformal curvature, a conformal geodesic can become trapped in smaller and smaller sets, or phrased informally: are spirals possible? We do not…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A…