Final answer:
Buffer analysis is the spatial analysis method used to calculate the number of people living within 800 meters of a library by creating a buffer zone and analyzing the population data within that zone.
Step-by-step explanation:
To determine the number of people living within a specific distance from a library, the spatial analysis method that would be used is buffer analysis. This method involves creating a buffer zone around the library at the specified distance of 800 meters and then analyzing the population data within this zone to ascertain the number of residents.
This technique is a standard functionality within Geographic Information Systems (GIS) software and allows geographers to quantify the number of people affected by or having access to certain facilities, like a library within a given radius.