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