This one is better

Torus: Freehand Guess in a Cube

This is my late night guess (with no actual observation). Tomorrow, I'll look at the model and see if I am close. I think I have to nail down the centers and the corners. Why are threes always so much harder than fours?

Torus: First Attempt

  This is my first attempt at drawing the torus knot. I don't know what I'm doing (is it obvious?) so I drew it freehand first, and then started to assign receding lines to three separate vanishing points. Now that I see it here, I think maybe a good next step would be to build a cube around it so I can plot the points on the vertical planes and well as the horizontal ones. I also see a little wobble in some of the lines, too. 

    Hmm...since the Rubik's' Cube is divided in threes, I wonder if those divisions of the cube would be helpful here?

   

A Torus Knot?

   This showed up in my mailbox today. It was a gift from the student who started my math journey by encouraging me to stop flying by the seat of my pants and actually plot spatial relationships when drawing forms with linear perspective. I am forever grateful for his gentle nudge in that direction.
    I've been asking him about this shape, which I think is called a torus knot. I told him I didn't understand the geometry at all, but I was going to make one out of clay so I could just draw it the old fashioned way. The next day, he presented me with this 3D printed model so that it might 'sate my curiosity and then I would stop pestering him'. 😐
     But still, I love the gift. I think drawing elongated ellipses on three different planes will be a good place to start on this problem. And I've purchased Geometry for Dummies. So in the future, I can maybe keep my pestering to a minimum.