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Advanced Math/how do apps calculate nearby supermarkets?


hello there - i would like to know, using a gps in mobile phones, how would i calculate from a certain location, how far out is a supermarket from me. i want to know say within a 10 mile radius how far a supermarket is from me?

what formula will I need to generate? Please help.

thank you.

A GPS will provide you with the traveling distance to the supermarket, but not the distance "as the crow flies." There are obstacles such as buildings and rivers that add to the distance calculated by the GPS.

You can obtain the latitude and longitude of the two points from the GPS, then use the Haversine formula to approximate the actual distance:

a = sin²(Δφ/2) + cos(φ1).cos(φ2).sin²(Δλ/2)
c = 2.atan2(√a, √(1−a))
d = R.c
where   φ is latitude, λ is longitude, R is earth’s radius (mean radius = 6,371km)
   note that angles need to be in radians to pass to trig functions!

The equations above are from

Note that the Haversine formula accounts for the overall curvature of the earth's surface, but not, of course, for local changes in elevation.  

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