I'm trying to use geohashes to group points from all over the US into "tiles". I'm using geohash 7, but I can't wrap my head around how a geohash "tile" in the north of the US would be the same size of one in the south due to the distortion of the globe. My question really is: can I assume that the size of a geohash 7 tile in the north of the US is the same size as one in the south?
The size of geotiles varies with latitude because the tiles are drawn on top of a rectangular projection of a sphere and there is no way to make such a projection without introducing significant distortion.
The most common projection tech folks run into is web Mercator. Tissot's indicatrix shows us that this projection is not equal area:
If you need equal area tiles for, eg, statistical purposes packages such as my dggridR provide this functionality by tiling a spherical representation of the Earth with hexagons, thereby inducing less distortion.