| 11. | So we identify ( or " glue together " ) antipodal points on the surface of the ball.
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| 12. | As noted above, the iterative solution to the inverse problem fails to converge or converges slowly for nearly antipodal points.
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| 13. | Each of the "'R "'3 lines in this construction intersects the sphere at two antipodal points.
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| 14. | At ten miles a day, you need 1250 days ( less than four years ) to traverse the distance between antipodal points.
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| 15. | Lines ( blue ) in the plane are mapped to great circles if one also includes one pair of antipodal points on the equator.
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| 16. | This is fine because each point in the ( open ) bottom hemisphere has an antipodal point in the ( closed ) top hemisphere.
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| 17. | The lines of "'RP "'2 will be the great circles of the sphere after this identification of antipodal points.
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| 18. | A great circle divides the earth into two hemispheres and if a great circle passes through a point it must pass through its antipodal point.
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| 19. | With this identification of antipodal points, the model satisfies Euclid's first postulate, which states that two points uniquely determine a line.
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| 20. | Their antipodal point is a bit off the coast of Washington .-- talk ) 03 : 00, 2 December 2013 ( UTC)
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