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Cross section (geometry)

 

 
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Cross section (geometry)
 
 
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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a cross-section is the intersection
Intersection (set theory)

In mathematics, the intersection of two Set A and B is the set that contains all elements of A that also belong to B , but no other elements....
 of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross-sections.

A cross-section, or section is also an orthographic projection
Orthographic projection

Orthographic projection is a means of representing a Three-dimensional space object in 2D.It is a form of parallel projection, where the view direction is orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface....
 of a 3-dimensional object from the position of a plane through the object. A floor plan
Floor plan

A floor plan, or floorplan, in architecture and building engineering is a diagram, usually to Scale , of the relationships between rooms, spaces and other physical features at one level of a structure....
 is a section viewed from the top.






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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a cross-section is the intersection
Intersection (set theory)

In mathematics, the intersection of two Set A and B is the set that contains all elements of A that also belong to B , but no other elements....
 of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross-sections.

A cross-section, or section is also an orthographic projection
Orthographic projection

Orthographic projection is a means of representing a Three-dimensional space object in 2D.It is a form of parallel projection, where the view direction is orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface....
 of a 3-dimensional object from the position of a plane through the object. A floor plan
Floor plan

A floor plan, or floorplan, in architecture and building engineering is a diagram, usually to Scale , of the relationships between rooms, spaces and other physical features at one level of a structure....
 is a section viewed from the top. In such views, the portion of the object in front of the plane is omitted to reveal what lies beyond. In the case of a floor plan, the roof and upper portion of the walls may be omitted.

Elevation
Elevation (view)

An elevation is an orthographic projection of a 3-dimensional object from the position of a horizontal plane beside an object. In other words, an elevation is a side-view as viewed from the front, back, left or right....
s or roof plans are orthographic projections, but they are not sections as their viewing plane is outside of the object.

With computed axial tomography, computers construct cross-sections from x-ray
X-ray

X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nanometers, corresponding to frequency in the range 30 Hertz to 30 Hertz and energies in the range 120 Electron volt to 120 keV....
 data.

A cross-section is a common method of depicting the internal arrangement of a 3-dimensional object in two dimensions. It is often used in technical drawing
Technical drawing

File:Drafter at work.jpgFile:Bundesarchiv B 145 Bild-F038800-0010, Wolfsburg, VW Autowerk.jpgTechnical drawing is the discipline of creating Standardization technology drawing by architects, CAD drafters, design engineers, and related professionals....
 and is traditionally crosshatched. The style of crosshatching indicates the type of material the section passes through.

Image:Cross section.png|A 3-D view of a beverage-can stove
Beverage-can stove

A beverage-can stove is a homemade, ultra-light portable stove. The simple design is made entirely from Aluminium can and burns alcohol, typically denatured alcohol....
 with a cross-section in yellow. Image:Seal_mechanical_compression.png|A 2-D cross-sectional view of a compression seal.

Cavalieri's principle
Cavalieri's principle

File:Cavalieri's principle.jpgIn geometry, Cavalieri's principle, sometimes called the method of indivisibles, named after Bonaventura Cavalieri, is as follows:...
 states that solids with corresponding cross-sections of equal areas have equal volumes.

See also

  • Descriptive geometry
    Descriptive geometry

    Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures....
  • Exploded view drawing
  • Graphical projection
    Graphical projection

    Graphical projection is a protocol by which an image of an imaginary Three-dimensional space object is projected onto a planar surface without the aid of mathematical calculation....
  • Plans (drawings)
    Plans (drawings)

    File:Lat?co?re 28.svgPlans are a set of two-dimensional diagrams or technical drawing used to describe a place or object, or to communicate building or fabrication instructions....