You open Yelp and tap restaurants near me.

Under a second later, you have a ranked list. Somewhere behind that tap, a system just searched 200 million businesses, found the handful within 500 metres of you, sorted them by distance, and shipped them back — while doing the same thing for a few thousand other people that second.

The obvious implementation is a WHERE clause on latitude and longitude. It does not work, and why it does not work is one of the more interesting failures in system design: the query is perfectly indexable in each dimension separately, and that turns out to be useless.