My drawing skills are pretty awful, and although I haven't yet had to teach multivariable calculus, someday I will. (And next semester in calculus II we're already doing some volumes by integrating cross sections, volumes and surface areas of rotation, etc). Is there a guide somewhere on how to draw standard 3D "math shapes" (sphere, torus, paraboloid of revolution, intersection of a cube with a plane through a given selection of three vertices, hyperboloid of two sheets, Möbius band, helix...)? I can sort of do a cube by drawing a square partially in front of another square, with some of the edges dotted, and connecting the corresponding vertices. That's about as far as it goes at present.

If there isn't such a guide specifically for math, I suppose I could (with much trepidation) look for more general books on drawing techniques...any ideas for a geodesic to get to math drawing?

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Dave Gaebler
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    Such a pathological inability never hindered any of my professors... – Emily Dec 19 '13 at 17:38
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    Honestly, learning how to draw in general helped me with technical diagrams and mathematical figures. Perhaps it's the only way... – Alex Nelson Dec 19 '13 at 17:48
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    I am terrible with drawing as well, but I can draw well enough so the students can see the pictures. One thing I'd recommend (in general) is to not add too much to a picture. For example, a sphere can be drawn as simply a circle and an equator, where the back half of the equator is dashed. Adding a longitude can make the picture worse. The same goes for any "round" shape (hyperboloids, paraboloid, etc.). Usually one can find specific tutorials on how to draw more complicated shapes (mobius band, torus, etc.) online. – RghtHndSd Dec 19 '13 at 17:49
  • After doing two quick internet searches "How to sketch a torus" and "How to sketch a mobius band", perhaps my last sentence is false. At least, it doesn't seem easy to find such tutorials. Perhaps this would make a good community wiki for math.SE where each answer has instructions/pictures of how to sketch individual mathematical shapes. – RghtHndSd Dec 19 '13 at 17:56
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    If you are a topologist it is okay if your circles look like squares. – Nicolas Bourbaki Dec 19 '13 at 18:01
  • You could always hire an artist to assist you with such sketches. – Karl Kroningfeld Dec 20 '13 at 00:20

1 Answers1


A Topological Picture Book by George K. Francis (Springer, 1988) comes vividly to mind.

Andrew D. Hwang
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  • I'd be interested to know why this suggestion merited a downvote. The book is instructive in the sense requested by the OP, and gorgeously-illustrated. It was such a memorable artistic epiphany for me as a student that it leapt out in regard to this question. – Andrew D. Hwang Dec 22 '13 at 18:08
  • I'd be interested to know that too. The book is at a more advanced level than I was looking for, but gives me something to aspire to. Thanks for the recommendation! – Dave Gaebler Jan 08 '14 at 18:02