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MF86: Newton's method and algebraic curves

Newton's method can be extended to meets of algebraic curves. We show how, using the examples of the Fermat curve and the Lemniscate of Bernoulli. We start by finding the Taylor expansions of the associated polynomials (polynumbers) at a fixed point (r,s) in the plane.The first tangents are viewed as tangent planes to the associated surfaces in three dimensional space (Interpretation B in the language of MF78).This is a more advanced lecture, and is the final lecture in this first part of this course. After this, we will turn our attention to the logical weaknesses of modern pure mathematics--of which there are many!
Length: 30:28

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