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- Cross_section_(geometry) abstract "In geometry, a cross section is the intersection of a figure in a 2-dimensional space with a line, or of a body in a 3-dimensional space with a plane, etc. When cutting an object into slices, one gets many parallel cross sections.Cavalieri's principle states that solids with corresponding cross sections of equal areas have equal volumes.The cross-sectional area of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has when viewed along its central axis, and when viewed from an orthogonal direction. A sphere of radius r has when viewed from any angle. More generically, can be calculated by evaluating the following surface integral: where is the unit vector pointing along the viewing direction toward the viewer, is a surface element with an outward-pointing normal, and the integral is taken only over the top-most surface, that part of the surface that is "visible" from the perspective of the viewer. For a convex body, each ray through the object from the viewer's perspective crosses just two surfaces. For such objects, the integral may be taken over the entire surface by taking the absolute value of the integrand (so that the "top" and "bottom" of the object do not subtract away, as would be required by the Divergence Theorem applied to the constant vector field ) and dividing by two:".
- Cross_section_(geometry) wikiPageID "1337370".
- Cross_section_(geometry) wikiPageRevisionID "587179495".
- Cross_section_(geometry) hasPhotoCollection Cross_section_(geometry).
- Cross_section_(geometry) subject Category:Elementary_geometry.
- Cross_section_(geometry) subject Category:Infographics.
- Cross_section_(geometry) subject Category:Methods_of_representation.
- Cross_section_(geometry) subject Category:Technical_drawing.
- Cross_section_(geometry) type Ability105616246.
- Cross_section_(geometry) type Abstraction100002137.
- Cross_section_(geometry) type Cognition100023271.
- Cross_section_(geometry) type Know-how105616786.
- Cross_section_(geometry) type Method105660268.
- Cross_section_(geometry) type MethodsOfRepresentation.
- Cross_section_(geometry) type PsychologicalFeature100023100.
- Cross_section_(geometry) comment "In geometry, a cross section is the intersection of a figure in a 2-dimensional space with a line, or of a body in a 3-dimensional space with a plane, etc. When cutting an object into slices, one gets many parallel cross sections.Cavalieri's principle states that solids with corresponding cross sections of equal areas have equal volumes.The cross-sectional area of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle.".
- Cross_section_(geometry) label "Cross section (geometry)".
- Cross_section_(geometry) label "Doorsnede (meetkunde)".
- Cross_section_(geometry) label "Przekrój poprzeczny".
- Cross_section_(geometry) label "Schnitt (Darstellung)".
- Cross_section_(geometry) label "Sección (geometría)".
- Cross_section_(geometry) label "Sezione (geometria)".
- Cross_section_(geometry) label "Разрез".
- Cross_section_(geometry) label "مقطع عرضي".
- Cross_section_(geometry) label "截面 (幾何)".
- Cross_section_(geometry) label "断面".
- Cross_section_(geometry) sameAs Schnitt_(Darstellung).
- Cross_section_(geometry) sameAs Sección_(geometría).
- Cross_section_(geometry) sameAs Sezione_(geometria).
- Cross_section_(geometry) sameAs 断面.
- Cross_section_(geometry) sameAs Doorsnede_(meetkunde).
- Cross_section_(geometry) sameAs Przekrój_poprzeczny.
- Cross_section_(geometry) sameAs m.04tt_h.
- Cross_section_(geometry) sameAs Q845080.
- Cross_section_(geometry) sameAs Q845080.
- Cross_section_(geometry) sameAs Cross_section_(geometry).
- Cross_section_(geometry) wasDerivedFrom Cross_section_(geometry)?oldid=587179495.
- Cross_section_(geometry) isPrimaryTopicOf Cross_section_(geometry).