TITLE: Can a tangle of arcs of ellipses interlock
QUESTION [12 upvotes]: This is a variation on an earlier question resolved by user35353: Can a tangle of arcs interlock? In that question, the arcs were restricted to circular arcs, and user35353's proof that one arc can be removed without disturbing the others relies on the circularity of the arcs. That proof fails with elliptical arcs.
The length of the major and minor axes are arbitrary, and, just as in the previous question, the arcs must leave a positive gap, i.e., they cannot be complete ellipses.

REPLY [13 votes]: Three tangled ellipses that can't be unlocked. The major radii of the smaller ellipses have to be a bit smaller than the minor radius of the large ellipse. The minor radii of the small ellipses have to allow them to be linked, but of course smaller than the large radius, so that they can't rotate.

Added
Let's consider an ellipse with radii $A,B$ $A\gt B$, and two identical ellipses with radii $a,b$, $a\gt b$. Assume that $a$ is very close to $B$, but still $a\lt B$.
Because $a\lt B$, there is a minimal distance $d$, so that, if we introduce the large ellipse through a small one, the distance between their centers cannot be smaller than $d$.
Because $a\gt b$, there is a maximal distance $D$, so that, if we introduce the large ellipse through a small one, and the distance between their centers is smaller than $D$, the small ellipse can't be rotated around the large one.
To find a configuration as in the figure which is locked, we look to satisfy the following conditions.

$b\gt d$, because we want the two small ellipses to be tangled.
$b\lt D$, because we want to prevent the rotation of the small ellipses around the large one.

To find the values satisfying these conditions, start from a configuration with $b\lt a\lt B\lt A$. Then, if the condition is not satisfied, replace $a\mapsto (a+B)/2$. Then, $d$ decreases, but $D$ remains unchanged, since it depends only on $b$. If we repeat this, $d\to 0$, so at some point $d\lt D$ and $d\lt b$. Then, $b$ can be replaced by a smaller value, which is larger than $d$, but smaller than $D$.