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Statements

Subject Item
dbr:Hedgehog_(geometry)
rdf:type
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Hedgehog (geometry)
rdfs:comment
In differential geometry, a hedgehog or plane hedgehog is a type of plane curve, the envelope of a family of lines determined by a support function. More intuitively, sufficiently well-behaved hedgehogs are plane curves with one tangent line in each oriented direction. A projective hedgehog is a restricted type of hedgehog, defined from an anti-symmetric support function, and (again when sufficiently well-behaved) forms a curve with one tangent line in each direction, regardless of orientation. Hedgehogs can also be defined from support functions of hyperplanes in higher dimensions.
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dbr:Hedgehog_(hypergraph) dbr:Hedgehog_space
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dbc:Plane_curves dbc:Differential_geometry
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1123571640
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dbr:Simple_closed_curve dbr:Pointwise dbr:Cusp_(singularity) dbr:Support_function n9:Polygonal_case_in_the_plane.png dbr:Deltoid_curve dbr:Fractal dbr:Parametric_equation dbr:Envelope_(mathematics) dbr:Plane_curve dbr:Convex_hull dbc:Plane_curves dbr:Weierstrass_function dbr:Convex_curve dbr:Astroid dbr:Differential_geometry n9:Reuleaux_middle_hedgehog.svg n9:Case_of_smooth_convex_bodies_with_positive_Gauss_curvature.png dbr:Continuously_differentiable_function dbr:Minkowski_addition dbc:Differential_geometry dbr:Leonhard_Euler n9:Astroid_as_envelope.png n9:Estrella_EpicicloidalRadioGeneratriz_y_Directriz.png dbr:Supporting_line dbr:Medial_triangle n9:Kakeya_needle.gif dbr:Origin_(mathematics) dbr:Line_segment dbr:Involute dbr:Curve_of_constant_width
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In differential geometry, a hedgehog or plane hedgehog is a type of plane curve, the envelope of a family of lines determined by a support function. More intuitively, sufficiently well-behaved hedgehogs are plane curves with one tangent line in each oriented direction. A projective hedgehog is a restricted type of hedgehog, defined from an anti-symmetric support function, and (again when sufficiently well-behaved) forms a curve with one tangent line in each direction, regardless of orientation. Every closed strictly convex curve, the envelope of its supporting lines. The astroid forms a non-convex hedgehog, and the deltoid curve forms a projective hedgehog. Hedgehogs can also be defined from support functions of hyperplanes in higher dimensions.
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