# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2023-02-15 00:30:05

mathdrop
Member
Registered: 2022-03-07
Posts: 73

### Torus projection

I'm after the equations of the projection
of a rotated torus on the xy-plane.

Imagine you have a donut,
which is shaped like a torus.

Now you symetrically poke it on a stick,
so the stick goes twice through the donut.

You place the stick before the x-axis and rotate it
with a light source before it.

See the borders of the shadow of the donut ?
I would like to find the equations of them.

If the donut is paralel to the xy-plane, you have 2 circles.
One bigger and one smaller.

If the donut is paralell to the xz-plane, you have 1 circle,
cut, pulled apart along x and a rectangle in between.

What if the donut is rotated by 45° ?
What if the donut is rotated by another angle ?

@Bob:
Thank you for helping me with the sphube-line intersection.
I would need some more time, there.

Offline