poikkipinnan

Poikkipinnan is a Finnish term for cross-section. It refers to the shape formed when a solid object is cut by a plane, or to the surface that is the intersection of the plane with the object. In mathematical terms, if S is a solid in three-dimensional space and P is a plane, the cross-section is the set S ∩ P, which is typically a two-dimensional figure whose form depends on the position and orientation of the plane. Cross-sections can be used to analyze properties by slicing a 3D object into 2D profiles. In geometry, familiar results include that a plane perpendicular to a cylinder yields a circle, while an oblique plane can yield an ellipse; a cone intersected by a plane may produce a circle, ellipse, parabola, or hyperbola depending on the plane.

In applications, the concept is central to volume calculation by slicing (Cavalieri principle) and to the analysis of geometric properties such as area and centroid of the cross-section. In engineering and structural analysis, cross-sectional shapes determine area A, centroid, and moments of inertia I_x, I_y, essential for bending and torsion calculations. In anatomy, poikkipinnan can describe transverse or other anatomical planes that define cross-sections of tissues and organs.

The term emphasizes the relationship between a three-dimensional object and a two-dimensional profile, and is widely used in Finnish technical vocabulary across mathematics, engineering, and science contexts.