Can someone explain how flat circles cannot be made into Borromean Rings? Perhaps I do not know what "flat circles" are?
Assume that the upper most circle in the picture above is "A". The lower most circle is "B" and the right most circle is "C".
In the picture above we have the following:
1) A is over B 2) A is under C 3) B is over C 4) B is under A 5) C is over A 6) C is under B
(Once can see that 1 and 4, 2 and 5 & 3 and 6 are merely saying the same thing in the opposite manner.)
I cut three identical circles out of a piece of paper and the cut a slit in each one to allow for interlocking. (One must assume a slit in the circle because one cannot (if not an illusionist, a magician with trick rings or a physicist with quantum mechanical rings) make solid objects pass through each other.) After doing so I was able to construct a BR immediately. No twisting, kinks or deformations were necessary - the feat was accomplished by merely passing the slits through at the appropriate points.
Now perhaps by flat circles it is meant that the circles are always on the same plane such that they would bump into each other and therefore interlocking could not occur. However, if that were the case you would have to say that two flat circles could not interlock. The implication would then be that BRs aren't that special; therefore, I have to assume that flat circles mean something else (and cause the impossibility of creating BRs) or that I have missed something that is blatantly obvious.
Assume that the upper most circle in the picture above is "A". The lower most circle is "B" and the right most circle is "C".
In the picture above we have the following:
1) A is over B
2) A is under C
3) B is over C
4) B is under A
5) C is over A
6) C is under B
(Once can see that 1 and 4, 2 and 5 & 3 and 6 are merely saying the same thing in the opposite manner.)
I cut three identical circles out of a piece of paper and the cut a slit in each one to allow for interlocking. (One must assume a slit in the circle because one cannot (if not an illusionist, a magician with trick rings or a physicist with quantum mechanical rings) make solid objects pass through each other.) After doing so I was able to construct a BR immediately. No twisting, kinks or deformations were necessary - the feat was accomplished by merely passing the slits through at the appropriate points.
Now perhaps by flat circles it is meant that the circles are always on the same plane such that they would bump into each other and therefore interlocking could not occur. However, if that were the case you would have to say that two flat circles could not interlock. The implication would then be that BRs aren't that special; therefore, I have to assume that flat circles mean something else (and cause the impossibility of creating BRs) or that I have missed something that is blatantly obvious.
I fear in my naiveté that a "flat circle" in the "physical" world; i.e., that I can cut out of a flat sheet of paper, is not the same as a flat circle in the scientific world.
Thanks!!