Paper cutting (ConceptTopic, 4)

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Revision as of 17:40, 31 August 2008 by Hayate (Talk | contribs)
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This page documents the results cutting a twisted loop of paper through the middle of the strip.

http://img59.exs.cx/img59/2479/cut.png

  • A 0-twist (hose) goes to two separate 0-twists:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/soxSJ0Juv_9r0-TIzZ910sIspypjShsJxD50b8ZrEYn020zL.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png
  • A 2-twist goes to two linked together 2-twists:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/gyt5tIm7re4Jnf4p10g4C0YORmn86u1j8krfgIU42nmKeG8T.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/TPHSzEkrzMf5nW_5ILVBWp0Zb8nbe0Ud1Mh7vcGcqlu0cyOk.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/4ci7taOw1EfPsscuIhxdCFyTkQ1HelwW9j78EVtdpIViA9ZJ.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/ET_Axau-K9zuB2hAzCqUlj29JC1BD4ybV0pc4oJKQI04bnA5.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png
  • A 3-twist goes to a long 8-twist containing a trefoil knot:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/aOEhZlheYnjndvXEJdcqRk_Hhn8cQmc3Ovz4m6KRjz6poBpZ.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/0d3bSe0uKc1MamcXOwHh8Me4WNk3dheDzdsYKy5DnDIopOWC.png
  • A 4-twist goes to two linked together 4-twists:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/gyt5tIm7re4Jnf4p10g4C0YORmn86u1j8krfgIU42nmKeG8T.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/TPHSzEkrzMf5nW_5ILVBWp0Zb8nbe0Ud1Mh7vcGcqlu0cyOk.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/4ci7taOw1EfPsscuIhxdCFyTkQ1HelwW9j78EVtdpIViA9ZJ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/ET_Axau-K9zuB2hAzCqUlj29JC1BD4ybV0pc4oJKQI04bnA5.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png
  • A 5-twist goes to a long 12-twist containing a knot with five crossings:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png ?
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/bS7C9Pqrcl14xaeiimbdNGcsPkBTfuCupg5LKcprKc9HRers.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png ?
  • A 6-twist goes to two linked together 6-twists:
http://teamikaria.com/dl/qjNL1AqhdfJF-QuxIA34_ywBleTcHIRDzoffL-mE8PIEobT8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png http://teamikaria.com/dl/qNLCl5smjE7qcLtT2YKMEeAUd8UIdjgSXRWClis5GOhTQY8V.png http://teamikaria.com/dl/gyt5tIm7re4Jnf4p10g4C0YORmn86u1j8krfgIU42nmKeG8T.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/TPHSzEkrzMf5nW_5ILVBWp0Zb8nbe0Ud1Mh7vcGcqlu0cyOk.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/S21EOFzp_QnM1XXHgzoPjLkqSrONYOmCNYUrWDZSPxMMYzDP.png
http://teamikaria.com/dl/fGc2kryV3TGg3XfCUwfsbABN9x6q-BelEMdk3IGyEEZ3sro8.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png http://teamikaria.com/dl/TNhEm8Kxs-KOeLTHm5445t9BxD8CeeSBc82So4QefnJM-5h-.png http://teamikaria.com/dl/4ci7taOw1EfPsscuIhxdCFyTkQ1HelwW9j78EVtdpIViA9ZJ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/ET_Axau-K9zuB2hAzCqUlj29JC1BD4ybV0pc4oJKQI04bnA5.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/r7IsJgql2lV-Y9G8avi68lWszG_cpAtaXcThzmn523w_jyqQ.png http://teamikaria.com/dl/U809reKC6hAZFkID5iW849WEXHWLSHA3HUy_BySEO2qOCKua.png

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.

See also

Retrieved from "http://hi.gher.space/wiki/Paper_cutting"