Paper cutting (ConceptTopic, 4)
From Hi.gher. Space
(Difference between revisions)
m |
m (→Cutting in half: fix) |
||
Line 31: | Line 31: | ||
|} | |} | ||
- | *A 1-twist ([[Möbius strip]]) goes to a long | + | *A 1-twist ([[Möbius strip]]) goes to a long 4-twist: |
{|cellpadding="0" cellspacing="0" | {|cellpadding="0" cellspacing="0" | ||
Line 39: | Line 39: | ||
|http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png | |http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png | ||
|http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png | |http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png | ||
- | |http://teamikaria.com/dl/ | + | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png |
+ | |http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | ||
+ | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png | ||
|http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | |http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | ||
- | |http://teamikaria.com/dl/ | + | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png |
|http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png | |http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png | ||
|- | |- | ||
Line 49: | Line 51: | ||
|http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png | |http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png | ||
|http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png | |http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png | ||
- | |http://teamikaria.com/dl/ | + | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png |
|http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | |http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | ||
- | |http://teamikaria.com/dl/ | + | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png |
+ | |http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png | ||
+ | |http://teamikaria.com/dl/N9582deBW3jnU5oD5gNGWO_YurilHb259DrNNOc0LVllxHY7.png | ||
|http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png | |http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png | ||
|} | |} |
Revision as of 20:27, 31 August 2008
This page documents the results cutting a twisted loop of paper.
Cutting in half
http://img59.exs.cx/img59/2479/cut.png
- A 0-twist (hose) goes to two separate 0-twists:
- A 1-twist (Möbius strip) goes to a long 4-twist:
- A 2-twist goes to two linked together 2-twists:
- A 3-twist goes to a long 8-twist containing a trefoil knot:
- A 4-twist goes to two linked together 4-twists:
- A 5-twist goes to a long 12-twist containing a knot with five crossings:
- A 6-twist goes to two linked together 6-twists:
General rule
We can deduce that, when n > 1, cutting an n-twist will produce a single strip with n crossings and 2(n+1) twists if n is odd, or two linked strips each with n twists if n is even.
Cutting in thirds
It is easy to see that cutting a loop into thirds rather than in half would be the same as above for an even number of twists. Therefore, the following concerns only loops with odd numbers of twists.
- A 1-twist goes to a short 1-twist linked to a long 4-twist:
- A 3-twist goes to a short 3-twist linked to a long 8-twist containing a trefoil knot:
(There are more crossings between the two loops than shown above)
Repeated cuttings
- Cutting a 3-twist in half produces an 8-twist with a trefoil knot. Cutting this in half produces two interlinked 8-twists, each with their own trefoil knot, but also crossing in multiple other places.