Log Function on a Riemann Surface

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Pantea Ferdosian Log Function on a Riemann Surface Math 401; Mathematics Through 3D Printing George Mason University Bernhard Riemann, Gauss's student, made groundbreaking contributions in the mid-19th century. Riemann's first insight was that we need more than two complex planes to visualize some functions involving i. A Riemann Surface allows us to think in four dimensions. Riemann's big idea is that the domain of input values for our multi-function should not be a flat, two-dimensional plane. Instead, it should be a curved surface living in higher-dimensional space, a Riemann surface. A Riemann surface is a geometric object assembled from open subsets of the complex plane using holomorphic maps. They are crucial throughout geometry, analysis, and algebra. For instance, every Riemann surface can be described as a complex algebraic curve - the locus of zeroes of a polynomial in two complex variables. http://people.math.umass.edu/~phacking/697 This is how I solved for the real and imaginary parts of my equation. Please examine my code for more information. (First Image)