Rolling Simplexes and Their Commensurability. II (A Lemma on the Directrix and Focus)

Abstract

The law of central-square dynamics

$$ \left(x,y,z\right)^{{\prime\prime} }=\frac{4{\uppi}^2k}{{\left(\alpha \left(x-a\right)+\beta \left(y-b\right)+\gamma \left(z-c\right)+\delta \right)}^2}\left(x-a,y-b,z-c\right), $$

expressing the focusing of a plane wave at the point (a, b, c) is discussed and justified.