parabolikus

Parabolikus, or parabolic in English, is an adjective used to describe objects, shapes, or phenomena that are related to a parabola, a plane curve with a distinctive U shape. The term derives from Greek parabola, meaning “placing beside” or “comparison,” and was adopted in geometry to denote a specific conic section.

In mathematics, a parabola is the set of all points equidistant from a fixed point called the focus and a fixed line called the directrix. It has a single axis of symmetry and a vertex at the point where the axis meets the curve. Equations of parabolas can take several forms, including y = ax^2 + bx + c in Cartesian coordinates or the standard form (y − k) = a(x − h)^2 after a translation.

In optics and engineering, parabolic shapes are valued for their focus properties: parallel rays are reflected to a single focal point in parabolic mirrors and antennas, making parabolic dishes highly effective for satellite communications, radio telescopes, and solar collectors such as parabolic troughs.

In physics, under a constant gravitational field with negligible air resistance, projectile motion traces a parabolic trajectory. In celestial mechanics, a parabolic orbit (eccentricity equal to 1) marks the boundary between bound (elliptical) and unbound (hyperbolic) paths.

Other uses include parabolic reflectors in microphones and architectural designs that exploit the structural and aesthetic properties of parabolas. The concept also appears in computer graphics and numerical methods through parabolic interpolation and smoothing techniques.