Cross section (geometry)

In geometry and science, a cross section is the intersection of a body in three-dimensional space with a plane, or the analog in higher-dimensional space. Cutting an object into slices creates many parallel cross sections. A cross section of three-dimensional space that is parallel to two of the axes is a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points of equal altitude.

Conic sections

Conic sections – circles, ellipses, parabolas, and hyperbolas – are formed by cross-sections of a cone at various different angles, as seen in the diagram at left.

Any planar cross-section passing through the center of an ellipsoid forms an ellipse on its surface, which degenerates to a circle for sections perpendicular to a symmetry axis.

A cross-section of a cylinder is a circle if the cross-section is parallel to the cylinder's base, or an ellipse with non-zero eccentricity (see diagram at right) if it is neither parallel nor perpendicular to the base. If the cross-section is perpendicular to the base it consists of two parallel line segments (not shown) unless it is just tangent to the cylinder, in which case it is a single line segment.

Cross section

Cross section may refer to:

Cross section (physics)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made of discrete particles. The cross section of a particle is the same as the cross section of a hard object, if the probabilities of hitting them with a ray are the same. It is typically denoted σ and measured in units of area.

In scattering experiments, one is often interested in knowing how likely a given event occurs. However, the rate depends strongly on experimental variables such as the density of the target material, the intensity of the beam, or the area of overlap between the beam and the target material. To control for these mundane differences, one can factor out these variables, resulting in an area-like quantity known as the cross section.

Definition

Cross section is associated with a particular event (e.g. elastic collision, a specific chemical reaction, a specific nuclear reaction) involving a certain combination of beam (e.g. light, elementary particles, nuclei) and target material (e.g. colloids, gases, atoms, nuclei). Often there are additional factors that can affect the cross section in complicated ways, such as the energy of the beam.

Cross Section (album)

Cross Section is an album by American jazz pianist Billy Taylor featuring tracks recorded in 1953 and 1954 for the Prestige label. The album rereleased eight tracks from 1954 which had originally been issued on the 10-inch LP Billy Taylor Plays for DJs along with four Mambo sides from 1953.

Reception

Allmusic awarded the album 4 stars with its review by Scott Yanow stating, "the four originals (which alternate with standards) were all dedicated to disc jockeys of the time. The trio was pretty tight with Taylor in the lead and, although boppish, it also looked back toward the swing era... The four mambos are ideal both for listening and for dance music. An enjoyable set".

Track listing

All compositions by Billy Taylor except as indicated