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Statements

Subject Item
dbr:Intersection_between_a_sphere_and_a_cylinder
dbo:wikiPageWikiLink
dbr:Sphere–cylinder_intersection
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dbr:Sphere–cylinder_intersection
Subject Item
dbr:Sphere-cylinder_intersection
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dbr:Sphere–cylinder_intersection
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dbr:Sphere–cylinder_intersection
Subject Item
dbr:Sphere–cylinder_intersection
rdfs:label
Sphere–cylinder intersection
rdfs:comment
In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve. For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the z-axis; points on the cylinder (with radius ) satisfy We also assume that the sphere, with radius is centered at a point on the positive x-axis, at point . Its points satisfy The intersection is the collection of points satisfying both equations.
foaf:depiction
n12:Viviani_curve.png
dcterms:subject
dbc:Geometric_intersection dbc:Analytic_geometry dbc:Spherical_curves dbc:Spherical_geometry
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32364281
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1116265728
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dbr:Cylinder_(geometry) dbc:Spherical_geometry dbr:Circle dbc:Spherical_curves dbc:Analytic_geometry dbc:Geometric_intersection n9:Viviani_curve.png dbr:Point_(geometry) dbr:Analytic_geometry dbr:Sphere dbr:Empty_set dbr:Viviani's_curve dbr:Without_loss_of_generality
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n12:Viviani_curve.png?width=300
dbo:abstract
In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve. For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the z-axis; points on the cylinder (with radius ) satisfy We also assume that the sphere, with radius is centered at a point on the positive x-axis, at point . Its points satisfy The intersection is the collection of points satisfying both equations.
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wikipedia-en:Sphere–cylinder_intersection?oldid=1116265728&ns=0
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5687
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wikipedia-en:Sphere–cylinder_intersection
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wikipedia-en:Sphere–cylinder_intersection
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dbr:Sphere–cylinder_intersection