Poikkipinta

Poikkipinta, in geometry, is the two-dimensional figure obtained when a plane intersects a three-dimensional object. The cross-section is determined by the plane’s position and orientation relative to the object and can reveal internal features without disassembling the object.

For common solids, cross-sections vary with the geometry of the solid and the plane. A sphere cut by any plane yields a circle. A right circular cylinder can produce a circle (plane perpendicular to the axis), an ellipse (oblique plane), or a rectangle-like shape if the plane is parallel to the axis. A cone can yield a circle, ellipse, parabola, or hyperbola depending on the plane’s angle to the axis. For polyhedra such as a cube, a plane generally produces a polygonal cross-section, which may be a triangle, quadrilateral, pentagon, or hexagon depending on the cut.

Cross-sectional area is a key concept in engineering and science, influencing material distribution, structural analysis, and manufacturing. In tomography and medical imaging, cross-sections of bodies are used to reconstruct three-dimensional structures. In architecture and design, cross-sections help visualize internal features and how different parts relate spatially.

Historically, the study of cross-sections contributed to the development of conic sections, arising from plane cuts of a cone. The term poikkipinta is the Finnish designation for this geometric concept.