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==Layman Statement of the Conjecture==

==Layman Statement of the Conjecture==

The basic idea of the conjecture is that if strings, surfaces, and other geometric objects "loop around" a three dimensional space space in the same way they loop around what mathematicians call a "three sphere," then the space in question is a three sphere itself.

 

The Poincare conjecture is this:  the set of points at an equal radius from the center in four-dimensional space (known as a "three-dimensional sphere") is "simply connected," and the only compact, simply connected manifold in four-dimensional space is a comparable shape.

 

Put another way, the conjecture states that if strings, surfaces, and other geometric objects "loop around" a three dimensional space in the same way they loop around what mathematicians call a "three sphere" (see below), then the space in question is a three sphere itself.

===The Three Sphere===

===The Three Sphere===