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I'm working on adding geofences to a mobile application. I know the proper way of calculating distance between two points on a sphere is using the great-circle or Haversine formula. I don't know if using those formulas are needed for relatively small scale applications. This leads to my question.
At what point does the distance given by a great-circle calculation diverge significantly from a planar calculation?
For the purposes of this discussion assume greater than 5% error is significant.
The geofence is simply a center point and a radius. If the point is within the radius, by distance, it is considered within the boundaries of the fence.
I am not sure if it matters, but I'm just worried about circular geofences at this time with a user defined radius between 50 and 200 meters.