Find the distance in kilometres between two points on the surface of the earth. This is just the sort of problem stored functions were made for. For a first order approximation, ignore deviations of the earth's surface from the perfectly spherical. Then the distance in radians is given by a number of trigonometric formulas. ACOS and COS behave reasonably:
We need to convert degrees latitude and longitude to radians, and we need to know the length in km of one radian on the earth's surface, which is 6378.388. The function:
set log_bin_trust_function_creators=TRUE;
DROP FUNCTION IF EXISTS GeoDistKM;
DELIMITER 
CREATE FUNCTION GeoDistKM( lat1 FLOAT, lon1 FLOAT, lat2 FLOAT, lon2 FLOAT ) RETURNS float
BEGIN
DECLARE pi, q1, q2, q3 FLOAT;
DECLARE rads FLOAT DEFAULT 0;
SET pi = PI();
SET lat1 = lat1 * pi / 180;
SET lon1 = lon1 * pi / 180;
SET lat2 = lat2 * pi / 180;
SET lon2 = lon2 * pi / 180;
SET q1 = COS(lon1lon2);
SET q2 = COS(lat1lat2);
SET q3 = COS(lat1+lat2);
SET rads = ACOS( 0.5*((1.0+q1)*q2  (1.0q1)*q3) );
RETURN 6378.388 * rads;
END;

DELIMITER ;
 toronto to montreal (505km):
select geodistkm(43.6667,79.4167,45.5000,73.5833);
++
 geodistkm(43.6667,79.4167,45.5000,73.5833) 
++
 505.38836669921875 
++
(Setting log_bin_trust_function_creators is the most convenient way to step round determinacy conventions implemented since 5.0.6.)