LATENT REFERENCES / TAG2
Möbius Transformation
Original title: メビウス変換
This reference note belongs to Tag2 in Latent References, an archive curated by Keigo Yoshida. Its archive region is Klein bottles · Möbius strips. The note preserves its source text and links so that readers can trace the material behind the 3D map.
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English translation of the archived note. JP shows the original text. Source links and literal code are retained; the translation does not update or independently verify the source claims.
https://scrapbox.io/files/6592c488c0f6b30023da99c6.png
Möbius transformations usually, the extended complex plane obtained by adding just one point at infinity to the Gaussian plane.
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= C ∪ {∞} is treated as the domain on which it is defined. The extended complex plane can also be viewed as a sphere called the Riemann sphere, or as the complex projective line CP1. Every Möbius transformation is a bijective conformal transformation from the Riemann sphere to itself, and conversely such transformations must indeed be Möbius transformations.
https://scrapbox.io/files/6592c488c0f6b30023da99c6.png
メビウス変換は通例、ガウス平面にただひとつの無限遠点を付け加えて得られる拡張複素平面
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= C ∪ {∞} 上で定義されるものとして扱われる。拡張複素平面はリーマン球面と呼ばれる球面とみることもできるし、複素射影直線 CP1 とみることもできる。どんなメビウス変換も、リーマン球面からそれ自身への全単射な共形変換になり、また逆にそのような変換は実際にメビウス変換とならねばならない。
Source updated 2024-01-01 · Snapshot 2026-10-08
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- Möbius StripComputed lexical cosine similarity 0.241 · shared title, text, tags and references