I'm attempting to equip this finite space with a metric. The points in this space are defined as all the intersection points, (see image). I think the metric will be approximately the Euclidean metric because the grid looks almost like a uniform grid, but seems to imply some kind of curvature, so maybe the metric is proportional to the Euclidean metric? I'd be interested to find out what the metric of this space actually is, and how to derive it.
Questions:
$1)$ What kind of curvature does this space imply?
$2)$ Is the metric "approximately" Euclidean?
image1
