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Sort of a weird request but how do you authors of books create drawings and diagrams of 3D geometric things?

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You could use python, scipy, numpy and matplotlib to make you graphs. Alternatively use a commercial package like Matlab or Mathematica if your college/uni has licenses available for students.
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Inkscape
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A good option is to use pgf and tikz packages from latex
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Some draw it by hand, others use a cad program, and I am sure there are other options.
by
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I did also a thesis about manifold. And I did a lot of my illustrative figures just with powerpoint. You can do some great stuff with that in a little time.
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GNU Plot is pretty decent too. Definitely not the recommended way to use GNU Plot but I took long exposure shots of my IBM 5151 displaying parts of Riemann surfaces using GNU Plot.
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It is very common to use the LaTex/Tex environment to publish mathematical/technical papers and books.

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