Degree of the Gauss Map
Let p(x,y), q(x,y) be polynomials with rational coefficients without common factors, of degrees n1 and n2, and let F=(p, q).
Let A be a rectangle in the plane defined by
so that no zero of F lies its boundary , and does not vanish at its vertices.
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- Gauss map where S1 is the unit circle.
- G is continuous ( ).
- and S1 carry the counterclockwise orientation.
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Degree d of G : an integer indicating how many times is wrapped around S1 by G.