Rectangles of all sorts of sizes, not just this one.
2026-03-28 02:48:56.1774666136
Please could anyone give me a generalisation of a rectangle which has a diagonal passing through it?
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Some hints:
Consider $(p\times q)$-rectangles. Let ${\rm gcd}(p,q)=:d$. Make some drawings where $d>1$ ($d=3$ in your figure) and find out what happens.
It remains to discuss the case $d=1$. The diagonal of the $(p\times q)$-rectangle then crosses a certain total number $r$ of vertical or horizontal interior gridlines, but does not go through an interior lattice point. The number $r$ is in a simple relation with the number of squares the diagonal bisects.