4 ms·

Using the 4th Dimension, the two interlocking rings can be separated. However, what would be the equivalent puzzle for the 3rd dimension? What 2D system require

by DC-3 8y ago

Using the 4th Dimension, the two interlocking rings can be separated. However, what would be the equivalent puzzle for the 3rd dimension? What 2D system requires the 3rd dimension to be separable? Is there even an equivalent? Clearly a circle within a circle is one such system, but it corresponds to a ball wholly contained by another ball in 3D, not a pair of interlocking rings.

zwkrt 8y ago
It is not possible for two ring shapes to interlock in 2D so there is no directly isomorphic trick.
simias 8y ago
You can't have interlocking rings in 2D without having some kind of intersection. You have a similar problem with moebius rings and klein bottles: moebius rings are 2D objects but you have to represent them in a 3D world if you don't want them to be self-intersecting. If you attempt to represent a moebius ring in 2D it'll necessarily self-intersect. Klein bottles are the same thing but with an added dimensions: any representation of a klein bottle in 3D makes it look like it's going through itself, even though in 4D it wouldn't: http://s3files.core77.com/blog/images/2013/06/klein-bottle-02.jpg http://s3files.core77.com/blog/images/2013/06/klein-bottle-0... It's also true if you remove a dimension: a 1D moebius strip would simply be a circle, but if you try to draw it in 1D you end up with a segment where both halves of the circle are overlapped. So every time we have a N-dimensional object that can only be properly represented in N+1 dimensions. That's also the same reason you can't solve the problem of connected three objects to three other objects on a 2D planes without intersecting: A B C X Y Z You can't distribute a, b and c to x, y and z on a 2D plane without intersection. Topology is fun.
lifeformed 8y ago
It would be a ring with a stick through it. In a 2D slice down the middle, it would look like a donut with a circle (the slice of the stick) in the hole. The circle appears to be stuck inside it, with no way out in 2D. In 3D, you just pull the stick out of the ring.

by DC-3 8y ago

zwkrt 8y ago

It is not possible for two ring shapes to interlock in 2D so there is no directly isomorphic trick.

simias 8y ago

You can't have interlocking rings in 2D without having some kind of intersection. You have a similar problem with moebius rings and klein bottles: moebius rings are 2D objects but you have to represent them in a 3D world if you don't want them to be self-intersecting. If you attempt to represent a moebius ring in 2D it'll necessarily self-intersect. Klein bottles are the same thing but with an added dimensions: any representation of a klein bottle in 3D makes it look like it's going through itself, even though in 4D it wouldn't: http://s3files.core77.com/blog/images/2013/06/klein-bottle-02.jpg http://s3files.core77.com/blog/images/2013/06/klein-bottle-0... It's also true if you remove a dimension: a 1D moebius strip would simply be a circle, but if you try to draw it in 1D you end up with a segment where both halves of the circle are overlapped. So every time we have a N-dimensional object that can only be properly represented in N+1 dimensions. That's also the same reason you can't solve the problem of connected three objects to three other objects on a 2D planes without intersecting: A B C X Y Z You can't distribute a, b and c to x, y and z on a 2D plane without intersection. Topology is fun.

lifeformed 8y ago

It would be a ring with a stick through it. In a 2D slice down the middle, it would look like a donut with a circle (the slice of the stick) in the hole. The circle appears to be stuck inside it, with no way out in 2D. In 3D, you just pull the stick out of the ring.