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- Pedal_curve abstract "The pedal curve results from the orthogonal projection of a fixed point on the tangent lines of a given curve. More precisely, for a plane curve C and a given fixed pedal point P, the pedal curve of C is the locus of points X so that the line PX is perpendicular to a tangent T to the curve passing through the point X. Conversely, at any point R on the curve C, let T be the tangent line at that point R; then there is a unique point X on the tangent T which forms with the pedal point P a line perpendicular to the tangent T (for the special case when the fixed point P lies on the tangent T, the points X and P coincide) – the pedal curve is the set of such points X, called the foot of the perpendicular to the tangent T from the fixed point P, as the variable point R ranges over the curve C.Complementing the pedal curve, there is a unique point Y on the line normal to C at R so that PY is perpendicular to the normal, so PXRY is a (possibly degenerate) rectangle. The locus of points Y is called the contrapedal curve.The orthotomic of a curve is its pedal magnified by a factor of 2 so that the center of similarity is P. This is locus of the reflection of P through the tangent line T.The pedal curve is the first in a series of curves C1, C2, C3, etc., where C1 is the pedal of C, C2 is the pedal of C1, and so on. In this scheme, C1 is known as the first positive pedal of C, C2 is the second positive pedal of C, and so on. Going the other direction, C is the first negative pedal of C1, the second negative pedal of C2, etc.".
- Pedal_curve thumbnail PedalConstruction.svg?width=300.
- Pedal_curve wikiPageExternalLink v=onepage&q&f=false.
- Pedal_curve wikiPageExternalLink v=onepage&q&f=false.
- Pedal_curve wikiPageExternalLink v=onepage&f=false.
- Pedal_curve wikiPageExternalLink books?id=YcsKAAAAYAAJ.
- Pedal_curve wikiPageExternalLink podaire.shtml.
- Pedal_curve wikiPageID "845864".
- Pedal_curve wikiPageLength "13580".
- Pedal_curve wikiPageOutDegree "40".
- Pedal_curve wikiPageRevisionID "669633108".
- Pedal_curve wikiPageWikiLink Alfred_George_Greenhill.
- Pedal_curve wikiPageWikiLink Auxiliary_circle.
- Pedal_curve wikiPageWikiLink Cardioid.
- Pedal_curve wikiPageWikiLink Catacaustic.
- Pedal_curve wikiPageWikiLink Category:Curves.
- Pedal_curve wikiPageWikiLink Category:Differential_geometry.
- Pedal_curve wikiPageWikiLink Caustic_(mathematics).
- Pedal_curve wikiPageWikiLink Center_of_similarity.
- Pedal_curve wikiPageWikiLink Cissoid_of_Diocles.
- Pedal_curve wikiPageWikiLink Ellipse.
- Pedal_curve wikiPageWikiLink Envelope_(mathematics).
- Pedal_curve wikiPageWikiLink Evolute.
- Pedal_curve wikiPageWikiLink File:Contrapedal.gif.
- Pedal_curve wikiPageWikiLink File:PedalCurve1.gif.
- Pedal_curve wikiPageWikiLink File:PedalCurve3.gif.
- Pedal_curve wikiPageWikiLink George_Greenhill.
- Pedal_curve wikiPageWikiLink Hippopede.
- Pedal_curve wikiPageWikiLink Homothetic_center.
- Pedal_curve wikiPageWikiLink Instant_center_of_rotation.
- Pedal_curve wikiPageWikiLink Instant_centre_of_rotation.
- Pedal_curve wikiPageWikiLink Lemniscate_of_Bernoulli.
- Pedal_curve wikiPageWikiLink Limaçon.
- Pedal_curve wikiPageWikiLink Line_(geometry).
- Pedal_curve wikiPageWikiLink List_of_curves.
- Pedal_curve wikiPageWikiLink Locus_(mathematics).
- Pedal_curve wikiPageWikiLink Logarithmic_spiral.
- Pedal_curve wikiPageWikiLink Orthogonal_projection.
- Pedal_curve wikiPageWikiLink Parametric_curve.
- Pedal_curve wikiPageWikiLink Parametric_equation.
- Pedal_curve wikiPageWikiLink Pedal_equation.
- Pedal_curve wikiPageWikiLink Perpendicular.
- Pedal_curve wikiPageWikiLink Plane_curve.
- Pedal_curve wikiPageWikiLink Polar_coordinate_system.
- Pedal_curve wikiPageWikiLink Polar_coordinates.
- Pedal_curve wikiPageWikiLink Projection_(linear_algebra).
- Pedal_curve wikiPageWikiLink Roulette_(curve).
- Pedal_curve wikiPageWikiLink Sinusoidal_spiral.
- Pedal_curve wikiPageWikiLink Tangent.
- Pedal_curve wikiPageWikiLink Tangent_line.
- Pedal_curve wikiPageWikiLink Tangential_and_normal_components.
- Pedal_curve wikiPageWikiLink Tangential_angle.
- Pedal_curve wikiPageWikiLink File:PedalConstruction.svg.
- Pedal_curve wikiPageWikiLink File:PedalCurve2.gif.
- Pedal_curve wikiPageWikiLinkText "Pedal curve".
- Pedal_curve wikiPageWikiLinkText "pedal curve".
- Pedal_curve wikiPageWikiLinkText "pedal".
- Pedal_curve hasPhotoCollection Pedal_curve.
- Pedal_curve title "Contrapedal Curve".
- Pedal_curve title "Orthotomic".
- Pedal_curve title "Pedal Curve".
- Pedal_curve urlname "ContrapedalCurve".
- Pedal_curve urlname "Orthotomic".
- Pedal_curve urlname "PedalCurve".
- Pedal_curve wikiPageUsesTemplate Template:Cite_book.
- Pedal_curve wikiPageUsesTemplate Template:Commons_category.
- Pedal_curve wikiPageUsesTemplate Template:Differential_transforms_of_plane_curves.
- Pedal_curve wikiPageUsesTemplate Template:MathWorld.
- Pedal_curve wikiPageUsesTemplate Template:Refbegin.
- Pedal_curve wikiPageUsesTemplate Template:Refend.
- Pedal_curve wikiPageUsesTemplate Template:Reflist.
- Pedal_curve subject Category:Curves.
- Pedal_curve subject Category:Differential_geometry.
- Pedal_curve type Physic.
- Pedal_curve comment "The pedal curve results from the orthogonal projection of a fixed point on the tangent lines of a given curve. More precisely, for a plane curve C and a given fixed pedal point P, the pedal curve of C is the locus of points X so that the line PX is perpendicular to a tangent T to the curve passing through the point X.".
- Pedal_curve label "Pedal curve".
- Pedal_curve sameAs منحنى_المواقع.
- Pedal_curve sameAs Fußpunkt-Transformation.
- Pedal_curve sameAs Podaria.
- Pedal_curve sameAs Podaire.
- Pedal_curve sameAs Podaria.
- Pedal_curve sameAs Подера.
- Pedal_curve sameAs Voetpuntskromme.
- Pedal_curve sameAs Podera.
- Pedal_curve sameAs Podaria.
- Pedal_curve sameAs Curva_pedal.
- Pedal_curve sameAs m.03gkfp.
- Pedal_curve sameAs Podară.
- Pedal_curve sameAs Подера.
- Pedal_curve sameAs Nožiščna_krivulja.
- Pedal_curve sameAs Подера.
- Pedal_curve sameAs Q1423838.
- Pedal_curve sameAs Q1423838.
- Pedal_curve sameAs 垂足曲线.
- Pedal_curve wasDerivedFrom Pedal_curve?oldid=669633108.
- Pedal_curve depiction PedalConstruction.svg.
- Pedal_curve isPrimaryTopicOf Pedal_curve.