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Relevant Pages

  • Re: easiest and shortest proof of Jordan Curve theorem
    ... > Some circles on the torus have interiors whose points all lie on the ... > surface of the torus. ... > the torus whose interior are points that lie outside the torus itself. ... Fine, but given a circle on the torus, or any other surface, how do you ...
    (sci.math)
  • Re: easiest and shortest proof of Jordan Curve theorem
    ... >> surface of the torus. ... >> the torus whose interior are points that lie outside the torus itself. ... > Fine, but given a circle on the torus, or any other surface, how do you ... > circle on the sphere, ...
    (sci.math)
  • Re: easiest and shortest proof of Jordan Curve theorem
    ... I think you need to work on your spatial intuition. ... I know I failed with that definition of given two points make it act as a radius to sweep out an interior of a circle on the torus. ...
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  • Re: easiest and shortest proof of Jordan Curve theorem
    ... >> its radius on the surface of the object can sweep out an entire circle ... > A circle does not include the interior; ... > And such a thing is also called a contractible curve. ... the equator is contractible. ...
    (sci.math)