Three Dimensional Plots: surfaces, space curves, and a Riemann surface with SageMath

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This lecture introduces three dimensional plotting. In three dimensions, we make the important dimension between surfaces (which are two dimensional) and the space curves (which are one dimensional). Surfaces may be defined via one explicit equation, or one implicit equation, or in parameter form by three functions in two variables. Space curves in parameter form are defined by three functions in one variable. In implicit form, a space curve is the intersection of two surfaces. The first part of the lecture is a short slide presentation with the plots that are then made in a Jupyter notebook with a SageMath kernel. The third part of the lecture attempts to explain the visualization of a Riemann surface, on the example of the cubic root, which involves four real variables, respectively the real and imaginary parts of two complex variables. The coloring of the surface represents the imaginary part of one of the variables.
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