@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

@heafnerj
Joe Heafner wrote:
> <em> [...] concept of #InertialFrame in [... the ST] of #relativity https://arxiv.org/abs/2103.15570 </em>

So ... author Boris Čulina, who

- doesn't even acknowledge a distinction of "good #clock" vs. "bad #clock" (cmp. MTW, Fig. 1.9),

- much less #HowTo define + measure such a distinction by [#CoincidenceDeterminations](http://einsteinpapers.press.princeton.edu/vol6-trans/165?highlightText=coincidences),

is nevertheless https://arxiv.org/auth/show-endorsers/2103.15570 ?!? ...

Well, therefore, we have #mastodon

#HyperbolicMotion of participant \(A\) in a "flat #spacetime region", in terms of Minkowski coordinates \((t, x)\) (which are of course adapted to the geometric relations between members of an #InertialFrame \(\mathcal F\)):

\(x_{\mathcal F}[ \, A \, ] = (c^2/a) \, \left(\sqrt{1+(a/c\, t_{\mathcal F}[ \, A \, ])^2}-1\right) \)

which can be re-arranged to "the canonical form" of an [hyperbola equation](https://en.wikipedia.org/wiki/Hyperbola#Equation) (wrt. Cartesian coordinates).

(2/7) #Relativity #TeachRelativity

Here's my first very rudimentary attempt at sketching a #PingCoincidenceLattice consisting of 10 participants in the configuration of a 10-vertices elementary cell of a [tetrahedral-octahedral honeycomb]( https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb )

#Graphics #Mathematica #Relativity #SpaceTime #SpaceTimeCoincidences #InertialFrame