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

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**mathdrop****Member**- Registered: 2022-03-07
- Posts: 75

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

Pages: **1**