User:Knotopologynn: Difference between revisions

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I am a Japanese. My real name is Takahiro NAGASHIMA (長島 隆廣, 長島：NAGASHIMA, 隆廣：Takahiro).
I am a Japanese.
A regular image figure of knots and links as shown in below
A regular image figure of knots and links as shown in below
is contribution by Knotopologynn.
is contribution by Knotopologynn.
These images are called "Canal-knots" or "Canal-links".
These images are called "Canal-like images" only for this occasion. The rectangular images drawn below are examples.
{|
{|
|- valign=top
{{Knot View Template|
{{Knot View Template|
image = Knot-31.jpg|
image = Knot-31.jpg|
Line 19: Line 20:
image = Link-L11a1.jpg|
image = Link-L11a1.jpg|
text = Link L11a1. <noinclude>Back to [[L11a1]]</noinclude><br>
text = Link L11a1. <noinclude>Back to [[L11a1]]</noinclude><br>
}}
{{Knot View Template|
image = Knot-Kinoshita-Terasaka-two-lines.jpg|<!-- 他の方法で描いた 樹下-寺阪結び目の画像 -->
text = An image of the Kinoshita-Terasaka knot drawn by another method
}}
}}
|}
|}
The process of making "Canal-like images" is drawn below from image (a) to image (g).

{|
{|
|- valign=top
{{Knot View Template|
{{Knot View Template|
image = aa_KT_Knot.jpg|
image = aa_KT_Knot.jpg|
text = (a): The Kinoshita-Terasaka knot
text = aa_KT_Knot.
}}
}}
{{Knot View Template|
{{Knot View Template|
image = bb_KT_Knot.jpg|
image = bb_KT_Knot.jpg|
text = bb_KT_Knot.
text = (b): Checker coloring
}}
}}
{{Knot View Template|
{{Knot View Template|
image = cc_KT_Knot.jpg|
image = cc_KT_Knot.jpg|
text = (c): Illustration showing the method of deformation
text = cc_KT_Knot.
}}
}}
{{Knot View Template|
{{Knot View Template|
image = dd_KT_Knot.jpg|
image = dd_KT_Knot.jpg|
text = (d): Checker coloring after deformation
text = dd_KT_Knot.
}}
}}
{{Knot View Template|
{{Knot View Template|
image = ee_KT_Knot.jpg|
image = ee_KT_Knot.jpg|
text = (e): The image obtained by transforming the Kinoshita-Terasaka knot
text = ee_KT_Knot.
}}
}}
{{Knot View Template|
{{Knot View Template|
image = ff_KT_Knot.jpg|
image = ff_KT_Knot.jpg|
text = (f): New image obtained from the previous image (e) by the operation of transforming into a square shape
text = ff_KT_Knot.
}}
}}
{{Knot View Template|
{{Knot View Template|
image = gg_KT_Knot.jpg|
image = gg_KT_Knot.jpg|
text = gg_KT_Knot.
text = (g): The Kinoshita-Terasaka knot
}}
}}
|}
|}
全ての結び目と絡み目は，"Canal-like images"に変形する事が出来ます，そして，その変形法が，下記の論文に書かれています．
All knots and links can be transformed into "Canal-like images", and the transformations are described in the following paper.

上記の(a)から(g)までの詳しい方法が，下記の論文"結び目と絡み目の正則表示に関する規則的な描画法"に書かれています．
The detailed method from (a) to (g) above is described in the following paper "Regular Drawing Method for Regular Presentation of Knots and Links".

論文：[結び目と絡み目の正則表示に関する規則的な描画法]："Regular Drawing Method for Regular Presentation of Knots and Links"
⚫
https://researchmap.jp/multidatabases/multidatabase_contents/detail/263160/c1f5868cc1bf2c390ea0a94a9cd44476?frame_id=539358

現在は，"Canal-like images"を得る為のコンピューター・プログラムが，世界中には何処にも存在しません．
この事実によって，"Canal-like images"を得る為のコンピューター・プログラムを新しく創れば，それは，あなた自身の輝かしい実績になります．

At present, there are no computer programs anywhere in the world for obtaining "Canal-like images".

With this fact, if you create a new computer program to get "Canal-like images", it will be your own glorious achievement.

私自身は，コンピューター・プログラムが創れません．

I myself cannot create computer programs.




⚫
* e-mail address: texnagashima@kuc.biglobe.ne.jp
⚫
論文：[結び目と絡み目の正則表示に関する規則的な描画法]： https://researchmap.jp/multidatabases/multidatabase_contents/detail/263160/c1f5868cc1bf2c390ea0a94a9cd44476?frame_id=539358


* e-mail address: knotopologynn.was.takahiro@gmail.com


An e-mail address of Knotopologynn is as follows:
⚫
texnagashima@kuc.biglobe.ne.jp


[[Media：knots_2005tn_Knotopologynn.pdf.ogg]] <!-- PDFファイルには [[Media：File.ogg]] が使えないのか？ -->
[[Media：knots_2005tn_Knotopologynn.pdf.ogg]] (PDF file) <!-- PDFファイルには[[Media：File.ogg]]が使えないのか？ -->


[[Media：Knots_2006_Knotopologynn.pdf.ogg]]
[[Media：Knots_2006_Knotopologynn.pdf.ogg]] (PDF file)

Latest revision as of 03:31, 12 June 2021

I am a Japanese. My real name is Takahiro NAGASHIMA (長島 隆廣, 長島：NAGASHIMA, 隆廣：Takahiro). A regular image figure of knots and links as shown in below is contribution by Knotopologynn. These images are called "Canal-like images" only for this occasion. The rectangular images drawn below are examples.

Knot 3_1. Back to 3_1
Knot 8_21. Back to 8_21
Knot K11n42. Back to K11n42
Link L11a1. Back to L11a1
An image of the Kinoshita-Terasaka knot drawn by another method

The process of making "Canal-like images" is drawn below from image (a) to image (g).

(a): The Kinoshita-Terasaka knot
(b): Checker coloring
(c): Illustration showing the method of deformation
(d): Checker coloring after deformation
(e): The image obtained by transforming the Kinoshita-Terasaka knot
(f): New image obtained from the previous image (e) by the operation of transforming into a square shape
(g): The Kinoshita-Terasaka knot

全ての結び目と絡み目は，"Canal-like images"に変形する事が出来ます，そして，その変形法が，下記の論文に書かれています． All knots and links can be transformed into "Canal-like images", and the transformations are described in the following paper.

上記の(a)から(g)までの詳しい方法が，下記の論文"結び目と絡み目の正則表示に関する規則的な描画法"に書かれています． The detailed method from (a) to (g) above is described in the following paper "Regular Drawing Method for Regular Presentation of Knots and Links".

論文：[結び目と絡み目の正則表示に関する規則的な描画法]："Regular Drawing Method for Regular Presentation of Knots and Links" 

https://researchmap.jp/multidatabases/multidatabase_contents/detail/263160/c1f5868cc1bf2c390ea0a94a9cd44476?frame_id=539358

現在は，"Canal-like images"を得る為のコンピューター・プログラムが，世界中には何処にも存在しません． この事実によって，"Canal-like images"を得る為のコンピューター・プログラムを新しく創れば，それは，あなた自身の輝かしい実績になります．

At present, there are no computer programs anywhere in the world for obtaining "Canal-like images".

With this fact, if you create a new computer program to get "Canal-like images", it will be your own glorious achievement.

私自身は，コンピューター・プログラムが創れません．

I myself cannot create computer programs.


  • e-mail address: texnagashima@kuc.biglobe.ne.jp
  • e-mail address: knotopologynn.was.takahiro@gmail.com


Media：knots_2005tn_Knotopologynn.pdf.ogg (PDF file)

Media：Knots_2006_Knotopologynn.pdf.ogg (PDF file)

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