More examples of sums of (some) inradii that are [conjectured to be] constant in #Poncelet families: https://youtu.be/HnqqaqDf2mo https://youtu.be/DHTnBUQabZ4

So there should be some POV explaining all these invariants?..

Triangulate a cyclic polygon. “Japanese theorem”: the sum of inradii of triangles doesn't depend on the triangulation.

Moreover, this sum is constant in the “Poncelet family” of all polygons with the same incircle and circumcircle.

#poncelet #geometry

@ocfnash
http://olivernash.org/2018/07/08/poring-over-poncelet/index.html

Awesome!
I'd love to find out about #Poncelet generalizations or related results in 3+1 dimensional flat #MinkowskiSpace, with

- all relevant edges along light cones (Are those "singular" and perhaps problematic, even in 3+1 D ?), and

- the \(n\)-sided polygon generalized to a #PingCoincidenceLattice (cmp. my sketch https://mathstodon.xyz/@MisterRelativity/109435130217990848 )

#SpaceTime #InertialFrame #geometry #relativity