| 11. | I am interested in plane curves only.
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| 12. | The second generalized curvature is called "'torsion "'and measures the deviance of from being a plane curve.
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| 13. | I realize the formula only holds if the plane curve does not cross the axis of rotation.
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| 14. | Consider the affine plane curve defined by the equation y ^ 2 = x ^ 5 + 1.
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| 15. | It starts with a plane curve, and repeatedly applies birational transformations to the plane to improve the curve.
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| 16. | For example, the disjoint union of a Sierpinski carpet and a circle is also a universal plane curve.
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| 17. | The plane curves of degree 3 are called cubic plane curves and, if they are non-singular, elliptic curves.
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| 18. | Thus for " g " = 3 the canonical curves ( non-hyperelliptic case ) are quartic plane curves.
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| 19. | The plane curves of degree 3 are called cubic plane curves and, if they are non-singular, elliptic curves.
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| 20. | The affine focal set of a plane curve will cusp points ( semi-cubical palabara | semi-cubical parabolae ).
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