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Sorry in advance for lacking the appropriate terminology, please help me edit it in below.

Take thease basic shapes:

triangle, square, ..., octigon pyramid, cube simplex, hypercube 

Each flat surface of a cube is a square. The same applies to others in the rest of the table above.

{circle, sphere, hypersphere} also have a great deal in common with thease series.

Therefore, is it true to say that a surface of a sphere either is, or is in some respects, or can be thought of as being a circle, or more accurately a disc?

My thoughts as to how this could be:

A segment or slice isn't a surface.

Thanks Qiaochu Yuan, in topologically two discs can be used to form a sphere. Although they are not flat discs.

Perhaps as the number of sides approaches infinity, the shape of each side aproaches a circle, although it's apparent that circular surfaces do not fit together to form a sphere.

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    Well, you would be certainly interested in [Algebraic topology](http://en.wikipedia.org/wiki/Algebraic_topology) which in part deals with such 'common things'. I don't know if there is a good introductory book on this topic.2012-02-07

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Certainly it is possible to think of a sphere as being glued together from several disks (in mathematics "circle" refers to the object $x^2 + y^2 = 1$ rather than the object $x^2 + y^2 \le 1$, which is a disk). In fact it suffices to use two: the upper hemisphere and the lower hemisphere of a sphere are topologically disks, and gluing them together at their boundaries gives a sphere.

The study of topological spaces from this point of view used to be known as combinatorial topology, but nowadays it is subsumed under algebraic topology.

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    So as I suspected, appart from my proof above proving it's possible it's definitely impossible :¬P2012-02-08