21. Eddie arrives at the team's headquarters, referred to as the " Hypersphere " and is initially dismissed as a fanboy. 22. As the radius increases the curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a hyperplane. 23. As the radius increases the curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a hyperplane. 24. That is, as a proportion of the relevant unit hypersphere taken up by the generalized angle, or set expressed in spherical coordinates. 25. RS works by iteratively moving to better positions in the search-space, which are sampled from a hypersphere surrounding the current position. 26. That's the definition of a hypersphere ; a torus has positive curvature at some places along its surface, negative curvature at others. 27. Just as in the simpler example above, each rotation represented as a point on the hypersphere is matched by its antipodal point on that hypersphere. 28. Just as in the simpler example above, each rotation represented as a point on the hypersphere is matched by its antipodal point on that hypersphere . 29. It should be trivial to find the average distance for points inside a hypersphere . talk ) 01 : 48, 15 April 2007 ( UTC) 30. Some spheres are not hyperspheres : suppose " S " is a sphere in three-dimensional space, but it is a hypersphere in the plane.
