spherical lantern
This is a model of a collapsible spherical paper lantern. We assume that the circular rings that form the skeleton are evenly spread out along the vertical axis. Based on this assumption, we may explore how the size (or radius) of these circles varies.
The videos below show the original lantern and corresponding manipulation in the GeoGebra applet.
Note that small dots are marked on each ring of this white lantern for identification of the rings position when expanded and collapsed. These dots are more evenly vertically when the lantern is expanded, different from how they are aligned when collapsed.