For example, the fastest distance between two points is not a straight line, it's the cycloid, specifically the Brachistochrone curve [2]. This is the path light follows.
One common misconception of the cycloid is related to its arc-length. At first glance many assume the arc-length of the cycloid is equal to circumference of the circle, but this is not the case. The line-of-sight distance between the cycloid starting point A and ending point B is equal to 2πr, the circumference of the circle -- however the arc-length of the cycloid curve is 8r, which is an integer value given an integer radius. The cycloid curve is full of interesting properties, many yet to be discovered and all its implications are not yet fully understood.
Another interesting aspect of the cycloid is not only is it the fastest path, but no matter where two objects begin on the curve, they'll both traverse the curve at maximal/optimal speed and both will arrive at the bottom of the curve at the same time, regardless of the delta between their starting positions. This aspect of the cycloid is referred to as the Tautochrone curve [3].
So if you're looking for ways to distribute partitions or encode invariants in your models, data or otherwise, the geometrical aspects of elliptical and cycloidal curves are a good place to explore.
Grant did a 3Blue1Brown video with with Steven Strogatz on the Brachistochrone a few years back: https://www.youtube.com/watch?v=Cld0p3a43fU
And Vsauce did one with Adam Savage on the Brachistochrone where they build a mechanical model of one that shows it's the fastest/optimal path among different curves, and their experiment also shows the cycloid Tautochrone invariant property where objects begin up the curve at different distances apart and yet all arrive together simultaneously in constant time. https://www.youtube.com/watch?v=skvnj67YGmw
NB: Consider this, two seperate impulses of light beginning at different distances away from the observer, both impulses of light traveling along the optimal path at the optimal speed, and both arriving at the observer simultaneously, without bending time. And as shown above, on a cycloidal curve, this phenomenon is not unique to light.
[1] https://en.wikipedia.org/wiki/Cycloid