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A plane, a circle (or most other 2-d curves), a triangle (or any other polygon).

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When flyin from Florida to Philippine why does the shortest route pass through Alaska?

The answer lies in Non-Euclidean geometry (spherical geometry). Florida, the Philippines, and Alaska are three collinear points on a great circle, a great circle is the equivalent to a line in Euclidean(2-D) geometry. A great circle is also classified as the shortest distance from one point to another around a circle. Because the earth is round, the distance seen on a flat map is a lot further than the distance on a globe, due to distortion. Therefore, following the great circle that goes through the three collinear points of Florida, the Philippines, and Alaska, it is a shorter distance to fly over Alaska


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