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 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". We decide to call these images "Canal".
These images are called "Canal-like images" only for this occasion. The rectangular images drawn below are examples.
Everyone use the name of "Canal", too, please.
{|
{|
|- valign=top
{{Knot View Template|
{{Knot View Template|
image = Knot-31.jpg|
image = Knot-31.jpg|
Line 20: 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|
image = aa_KT_Knot.jpg|
text = (a): The Kinoshita-Terasaka knot
}}
{{Knot View Template|
image = bb_KT_Knot.jpg|
text = (b): Checker coloring
}}
{{Knot View Template|
image = cc_KT_Knot.jpg|
text = (c): Illustration showing the method of deformation
}}
{{Knot View Template|
image = dd_KT_Knot.jpg|
text = (d): Checker coloring after deformation
}}
{{Knot View Template|
image = ee_KT_Knot.jpg|
text = (e): The image obtained by transforming the Kinoshita-Terasaka knot
}}
{{Knot View Template|
image = ff_KT_Knot.jpg|
text = (f): New image obtained from the previous image (e) by the operation of transforming into a square shape
}}
{{Knot View Template|
image = gg_KT_Knot.jpg|
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．
An e-mail address of Knotopologynn is as follows:
All knots and links can be transformed into "Canal-like images", and the transformations are described in the following paper.
⚫
texnagashima(at)kuc.biglobe.ne.jp.

An image of all knots and links would be a regular image figure like these
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．
in the future.
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) <!-- PDFファイルには[[Media：File.ogg]]が使えないのか？ -->

[[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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