Halbzylinderförmige

Halbzylinderförmige refers to a geometric shape that is formed by cutting a complete cylinder in half along a diameter perpendicular to its axis. The resulting figure has a semicircular cross-section in the plane perpendicular to the axis and retains the full height of the original cylinder. In German, “Halbzylinderförmig” is an adjective meaning “half‑cylindrical shaped,” while “Halbzylinderförmige” can be used as a noun to describe an object with this shape.

The dimensions of a half‑cylinder are given by the radius r of the base, the height h along the axis, and the thickness t along the curved surface. The curved surface area equals πrt, whereas the total surface area includes the lateral seam formed by the cut and both end faces, giving A_total = πrt + 2rh + t h. The volume is half that of a full cylinder, V = ½πr²h. Because of the symmetry, the center of mass lies on the axis, at a distance r / 2 from the flat base.

Halbzylinderförmige structures appear in various engineering and architectural contexts. In civil engineering, road bridges often employ half‑cylindrical girders to achieve high strength with reduced material. In fluid mechanics, a half‑cylinder acts as a model shape for studying flow separation around semi‑cylindrical bodies. Dental prosthetics sometimes use half‑cylindrical molds to support crowns or bridges. In toys, half‑cylindrical shapes form the basis of many beam‑and‑block puzzles where the curved segment must align with a complementary flat face.

Mathematical studies of half‑cylinders cover topics such as eigenvalue problems for vibrating membranes, heat conduction in semi‑circular domains, and optimization of material usage. Despite its simple appearance, the half‑cylinder offers rich geometric and physical properties that make it a common subject in applied mathematics and design.