Assuming you have the latitude and longitude of your user, and you want to find nearby... let's say restaurants, how do you query your relational DB? For something like "restaurants within a 25 mile radius"?
Would you just query for restaurants in a square with a long and lat greater than/less than the user's loc +/- 25 miles (converted to degrees I guess), and then filter out the "corners" in whatever language your using? Or can/should you do it directly in the SQL?
Take a look at the spatial features available in oracle for instance - here is the wikipedia entry http://en.wikipedia.org/wiki/Spatial_query, and a link with examples from noaa https://www.ngdc.noaa.gov/wiki/index.php?title=Sample_Oracle_Spatial_Queries
Your "circle" will already be quite deformed if you are treating lat/long as a rectilinear grid any significant distance from the equator (like, say, in New York, or London, or Moscow). Trimming the corners off the "square" doesn't improve it much.
I know you specifically mentioned relational databases, but I would reco that you at least look into a system which has a native implementation of spacial querying.
Personally, I've found MongoDB to be pretty elegant: http://www.mongodb.org/display/DOCS/Geospatial+Indexing
Found a really good guide here: http://code.google.com/apis/maps/articles/phpsqlsearch.html
Much simpler than many of the other explanations...