I am trying to understand what happens in this gif video:
Source: http://9gag.com/gag/aAVp4V9/is-this-even-possible
It is quite interesting because at a first look, it was very counter-intuitive.
Assuming that the yellow glass is the $xy-$plane, at first I thought that this is the projection map: $\mathbb R^3 \to \mathbb R^2$. However, the projection of a line in $\mathbb R^3$ onto a plane must still be a line, but not a paralobic (or maybe hyperbolic or trigonometric) curve. So, this "thing" is not a projection, but something else.
What can be a function describing this situation? And what is the type (parabola, hyperbola, sine, circle etc.) of the curve on the glass?
A hyperboloid of one sheet is a doubly ruled surface; if it is a hyperboloid of revolution, it can also be obtained by revolving a line about a skew line.
Source: wiki