Point-line duality
= Point-line duality
{title2=$p\in\ell\Longleftrightarrow\ell^*\in p^*$}
A point $[a:b:c]$ of the <projective plane> corresponds to the dual line $aX+bY+cZ=0$. A line given by those coefficients corresponds back to the point $[a:b:c]$. Incidence is reversed: $p\in\ell$ if and only if $\ell^*\in p^*$. Thus collinear point triples become concurrent line triples, preserving the essential combinatorics of <incidence geometry>.