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With thanks to my mentor Foci of Algebraic Curves November 7, 2008 - - PDF document
With thanks to my mentor Foci of Algebraic Curves November 7, 2008 - - PDF document
11/23/2008 With thanks to my mentor Foci of Algebraic Curves November 7, 2008 Outline of Talk What are Foci? Plcker Formulation 1 11/23/2008 Example 1: The k ellipse The 3 ellipse The innermost curve is convex 2 11/23/2008 Non
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Non‐smooth example A 3‐ellipse with 8 (of nine) foci Example 2: Lemniscates Lemniscates can be anything E.T.: Phone Home!
des cassiniennes alien ... par Alain Esculier
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Example 3: Siebeck’s Theorem Bôcher‐Grace Theorem Class Three
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11/23/2008 5 Example 4: Non‐Euclidean polynomials
n = 4 example The hyperbolic ellipse
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Example 5: Eigenvalues Kippenhann’s Theorem Example of an RZ curve The dual curve
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RZ curves and their duals The dual of this RZ curve is not convex, but its convex hull is a numerical range Example 6: Schwarz Reflection
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Application: Quadrature Domains Conclusion: Foci are interesting
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The End