Stereographic Projection
Just as a two dimensional sphere embedded in three dimensions can be mapped onto a two-dimensional plane by a stereographic projection, an n-sphere can be mapped onto an n-dimensional hyperplane by the n-dimensional version of the stereographic projection. For example, the point on a two-dimensional sphere of radius 1 maps to the point on the plane. In other words,
Likewise, the stereographic projection of an n-sphere of radius 1 will map to the dimensional hyperplane perpendicular to the axis as
Read more about this topic: Hypersphere
Famous quotes containing the word projection:
“In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
—Nelson Goodman (b. 1906)