title: Calculate equidistant point with minimal distance from 3 points in N-dimensional space
body: <p>I'm trying to code the <a href="http://en.wikipedia.org/wiki/Bounding_sphere#Ritter.27s_bounding_sphere" rel="nofollow">Ritter's bounding sphere algorithm</a> in arbitrary dimensions, and I'm stuck on the part of creating a sphere which would have 3 given points on it's edge, or in other words, a sphere which would be defined by 3 points in N-dimensional space.</p>
  
  <p>That sphere's center would be the minimal-distance equidistant point from the (defining) 3 points.</p>
  
  <p>I know how to solve it in 2-D (circumcenter of a triangle defined by 3 points), and I've seen some vector calculations for 3D, but I don't know what the best method would be for N-D, and if it's even possible.</p>
  
  <p>(I'd also appreciate any other advice about the smallest bounding sphere calculations in ND, in case I'm going in the wrong direction.)</p>