Polynomial Lemniscate
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For any such polynomial p and positive real number c, we may define a set of complex numbers by p(z) = c. In general, a polynomial lemniscate will not touch at the origin, and will have only two ordinary n-fold singularities, and hence a genus of (n 1)2. As a real curve, it can have a number o...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For any such polynomial p and positive real number c, we may define a set of complex numbers by p(z) = c. In general, a polynomial lemniscate will not touch at the origin, and will have only two ordinary n-fold singularities, and hence a genus of (n 1)2. As a real curve, it can have a number of disconnected components. Hence, it will not look like a lemniscate, making the name something of a misnomer.
