crosssections

Cross sections are a way of describing what is obtained when a three-dimensional object is cut by a plane or, more generally, when a higher‑dimensional object is intersected by a lower‑dimensional one. In geometry, a cross section is the two‑dimensional shape that results from slicing a solid with a plane. The exact form of the cross section depends on the orientation of the plane and the original object; for example, slicing a sphere with a plane yields a circle, while slicing a cylinder parallel to its base yields a circle and slicing it obliquely yields an ellipse. Cross sections underpin the slicing method used to compute volumes, a consequence of Cavalieri’s principle: solids with identical cross‑sectional areas at all heights have equal volumes.

In physics, the term cross section has a different meaning. A cross section measures the probability of an interaction between particles and a target, such as scattering or absorption. The total cross section aggregates all possible interaction probabilities, while the differential cross section describes how these probabilities are distributed with respect to angles or energies. Cross sections are expressed in units of area, most commonly barns (10^-28 m^2). They are determined experimentally by comparing observed interaction rates to the incident particle flux and target density, and theoretical models aim to predict their energy and angle dependence.

Cross sections also appear in applied and imaging contexts. Cross‑sectional area is used in aerodynamics and hydrodynamics to estimate drag and flow resistance, and cross‑sectional imaging in medicine (such as CT or MRI) produces slices or cross sections through the body for diagnostic purposes.