User:Knotopologynn

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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)