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- Homothetic_transformation abstract "In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sendsin other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if λ > 0) or reverse (if λ < 0) the direction of all vectors. Together with the translations, all homotheties of an affine (or Euclidean) space form a group, the group of dilations or homothety-translations. These are precisely the affine transformations with the property that the image of every line L is a line parallel to L.In projective geometry, a homothetic transformation is a similarity transformation (i.e., fixes a given elliptic involution) that leaves the line at infinity pointwise invariant.In Euclidean geometry, a homothety of ratio λ multiplies distances between points by |λ| and all areas by λ2. The first number is called the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above mentioned fixed point S is called homothetic center or center of similarity or center of similitude".
- Homothetic_transformation thumbnail Geom_podobnost_stejnolehlest.svg?width=300.
- Homothetic_transformation wikiPageExternalLink Homothety.shtml.
- Homothetic_transformation wikiPageID "386138".
- Homothetic_transformation wikiPageRevisionID "603057777".
- Homothetic_transformation hasPhotoCollection Homothetic_transformation.
- Homothetic_transformation subject Category:Transformation_(function).
- Homothetic_transformation comment "In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sendsin other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if λ > 0) or reverse (if λ < 0) the direction of all vectors.".
- Homothetic_transformation label "Homotecia".
- Homothetic_transformation label "Homotetia".
- Homothetic_transformation label "Homothetic transformation".
- Homothetic_transformation label "Homothetie".
- Homothetic_transformation label "Homothétie".
- Homothetic_transformation label "Jednokładność".
- Homothetic_transformation label "Omotetia".
- Homothetic_transformation label "Vermenigvuldiging (meetkunde)".
- Homothetic_transformation label "Гомотетия".
- Homothetic_transformation label "تحاك".
- Homothetic_transformation sameAs Homothetie.
- Homothetic_transformation sameAs Ομοιοθεσία.
- Homothetic_transformation sameAs Homotecia.
- Homothetic_transformation sameAs Homothétie.
- Homothetic_transformation sameAs Omotetia.
- Homothetic_transformation sameAs Vermenigvuldiging_(meetkunde).
- Homothetic_transformation sameAs Jednokładność.
- Homothetic_transformation sameAs Homotetia.
- Homothetic_transformation sameAs m.0226bb.
- Homothetic_transformation sameAs Q583960.
- Homothetic_transformation sameAs Q583960.
- Homothetic_transformation wasDerivedFrom Homothetic_transformation?oldid=603057777.
- Homothetic_transformation depiction Geom_podobnost_stejnolehlest.svg.
- Homothetic_transformation isPrimaryTopicOf Homothetic_transformation.
