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Functions homo/isomorphic to change in scale

  1. May 28, 2010 #1
    I would like to find out which functions retain the same structure when they are scaled. Particularly I am interested in projections.

    For example, a parabola 3d space viewed at another angle can still be represented by at^2 + bt+c. A circle however can not (ellipse)

    I am guessing conic sections have this property? Are there any other functions that have this property, and what terms are associated with this property?

    Attached Files:

  2. jcsd
  3. May 28, 2010 #2
    I think it would help looking at projective surfaces, with homogeneous coordinates.
  4. May 29, 2010 #3


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    Have what property? You assert that a parabola, projected onto any plane, is still a parabola (which is not quite true- it can project to a ray) while that is not true for a circle. But parabola and circle are both conic sections.
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