I have to do some homework questions that require me to draw graphs on a torus. My drawing skills suck, so I wondered if there is a program which allows you to do something like this easily?
[Math] How to manually draw graphs on a torus
graph theorymath-software
Best Answer
Some tips:
Instead of drawing on a torus, it's enough to draw on a topologically equivalent shape (e.g. a surface of a regular 3D object with a hole, like a mug where the hole is between the mug and its handle).
To help your imagination, just cut out a piece of paper and make (cut out) a hole in it, and draw your graph on it (and be aware you can go over the edge to the other side).
You could try to draw your graph on a plane with a bridge (like a regular real-life bridge): there are two places where the bridge starts and ends and you can go over the bridge without crossing the edges underneath it.
You could try to draw your graph on a simplified net of a torus, in particular two disks with holes (remember the outer and inner edges of the disks will be glued together).
The best approach in my opinion would be to use just a normal rectangle with edges glued together (you glue together the horizontal edges and then also the vertical edges), it is a special case of simplified net of a torus. It means, that when you go over the edge, you come back from the other side (although mind your orientations, on the other side you "reappear" exactly at the same position you reached the first side).
All the above pictures were created with Inkscape. You can find sources here (download raw and open in Inkscape): 1, 2, 3, 4, 5.
I hope this helps $\ddot\smile$