What is the figure in this animation called?
The black dot is mid point of the green line segment joining the purple dot & the green dot. The green dot rotates 5 times as fast as the purple dot. The locus of the black dot is the red curve.
- What is this red curve called?
- Where to learn more about it?
- What are applications of it?
- In which field this is used?
This appears to be similar to an epitrochoid, which is given by
$$ x=m\cos(t)-h\cos(mt/b)\\ y=m\sin(t)-h\sin(mt/b) $$
where $t\in[0,2\pi]$. In this case, $m=h=10 \text{ and } b=2$. The figure below shows the results for various cases of $m=h \text{ and } b=2$.
Technically, the epitrochoid is the roulette of a point $P$ attached to a circle $S$ rolling about the outside of a fixed circle $C$. See, for example, A Catalog of Special Plane Curves, J. Dennis Lawrence, Dover, 1972.