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Mathematics Forum
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| Author | Message / Information |
| cramwit Quote | Reply | | Eversion of a Sphere? posted on: 3/27/2007 10:27:44 PM Eversion of a sphere? You push each side of the sphere in past itself creating the inverted sphere in the middle with a non-inverted inner-tube around it. You work & swell the inverted sphere out to the edge of the non-inverted inner-tube changing it into a horned 'C' shape around the inverted sphere [egg shape]. You work the inverted sphere around the 'C' shape in an eccentric [outside faster than inside] way so the inverted sphere becomes the wrap around horned 'C' shape. You create an inverted inner-tube around the now non-inverted inner sphere. Then you just release the inner non-inverted sphere to pass through itself & you have the inverted sphere. I think that might be correct, but i am not quite sure. |
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cramwit
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Eversion of a Sphere?
replied on: 3/28/2007 7:45:25 PM I am wrong. the horn points create a pinch point. I think the difficulty in the eversion of a sphere is that by trying to do it smoothly it requires that the space adjacent to any portion of the sphere must slide away to be removed. But because the sphere bifurcates a/the 3D space & a tear or rip is not allowed there is no way the adjacent space from inside the sphere can slide to the outside & visa versa. So neither can the interior slide to the exterior & visa versa. Therefore i am pretty sure there is no way, without accessing a 4th dimension, to 'smoothly' evert the sphere. If you do the corollary in 2D, everting a circle in a plane you can rotate all points of the circle without it leaving the plane and without breaking the circle, but it does require utility of a higher dimension. Also it leaves the circles points with a fundamentally altered relationship in the plane. They have swapped which side of themselves face which side of the bifurcated 3D space. |
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