Editing Hyperplane (section)

===Projective hyperplanes===
'''Projective hyperplanes''', are used in [[projective geometry]].  A [[Projective geometry#Projective subspace|projective subspace]] is a set of points with the property that for any two points of the set, all the points on the line determined by the two points are contained in the set.<ref>{{citation|first1=Albrecht|last1=Beutelspacher|first2=Ute|last2=Rosenbaum|title=Projective Geometry: From Foundations to Applications|year=1998|publisher=Cambridge University Press|isbn=9780521483643|page=10}}</ref> Projective geometry can be viewed as [[affine geometry]] with [[vanishing point]]s (points at infinity) added.  An affine hyperplane together with the associated points at infinity forms a projective hyperplane.  One special case of a projective hyperplane is the '''infinite''' or '''ideal hyperplane''', which is defined with the set of all points at infinity.

In  projective space, a hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space.  The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other.