projectively In A Sentence
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- In the case of a parabola, that is, when, there is no center since the above denominators become zero ( or, interpreted projectively, the center is on the line at infinity .).
- However, any two conic sections are projectively equivalent.
- So a parabola and ellipse are the " same " when thought of projectively, but different when regarded as affine objects.
- The projectively extended real line must not be confused with the extended real number line, in which and are distinct.
- The ovals obtained by removing a point from a hyperoval are projectively equivalent if and only if the removed points are in the same orbit of the automorphism group of the hyperoval.
- The projectively extended real line may be identified with the projective line over the reals in which three specific points ( e . g ., and ) have been chosen.
- However, within PSL ( 2, mathbb Z ) this is the group of automorphisms of the quadratic form x ^ 2 + y ^ 2 + xy whose zeros ( projectively ) are the cube roots of unity.
- Rather they are projectively parametrized, meaning that their preferred class of parameterizations is acted upon by the group of fractional linear transformations.
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