Radgeometrie

Radgeometrie is a term used in geometry to describe an approach that emphasizes measurements and relationships with respect to a fixed center point. In this view, many constructions and analyses are conducted in terms of radii, circles, and radial symmetry, rather than solely by Cartesian coordinates. The concept is applicable to two-dimensional plane geometry and, in extended form, to higher dimensions through spheres and hyperspheres. While not always established as a formal separate discipline, Radgeometrie serves as a practical framework for problems where radial distance and angular position are primary.

Core notions include the radius as a distance from the center to a point, the circle as the locus of points at a fixed distance, and the sector or arc formed between radii. Radial symmetry refers to figures that look the same under rotations around the center. Representations often use polar coordinates, where a point is described by (r, theta) and the relation to Cartesian coordinates is x = r cos theta, y = r sin theta. Radial functions describe how the radius varies with angle, r = f(theta).

Methods combine analytic geometry with geometric constructions: transformations between coordinate systems, analysis of symmetry, and the study of curves defined by radial constraints. Typical problems include determining areas and lengths of shapes bounded by circles and radial lines, and designing patterns with circular or radial regularity.

Applications span design and architecture, computer graphics and visualization, robotics and sensor layouts, and geographic or astronomical mappings that rely on circular or polar layouts. The term remains mainly descriptive, guiding intuition for problems centered on a common origin rather than a distinct axiomatic theory.