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Polar v Constant Latitude routes

Compare the distance between two points diametrically opposite each other on a line of latitude by travelling around the line of latitude in the first case and by travelling directly over the nearest pole along a line of longitude in the other case.

Make this comparison for different lines of latitude and show that the ratio of the distances tends to a limit as the lines of latitude get nearer to the pole.

The Earth Animation requires Flash Player version 9. Click on the Earth to draw the lines of latitude and longitude. Move the mouse pointer to the window edges to navigate.