Difference between r1.13 and the current

@@ -77,7 +77,10 @@

Kähler
Ggl:Kähler
Naver:Kähler

Kähler_manifold ~~///~~ WtKo:ä = https://ko.wiktionary.org/wiki/ä https://ko.wikipedia.org/wiki/움라우트 - 그럼 ae로 표현?

Kähler_manifold

WtKo:ä = https://ko.wiktionary.org/wiki/ä

WtEn:ä

https://ko.wikipedia.org/wiki/움라우트 - 그럼 ae로 표현?

Kahler_manifold or
Kaehler_manifold - pagename TBD. WtEn:ä Ndict:ä Naver:ä Bing:ä Ggl:ä Ggl:ä+transliteration Naver:ä+표기 Ggl:ä+표기
[[WpEn:Kähler_manifold]]

@@ -94,10 +97,16 @@

WpEn:manifold_learning ffffffff

... Google:manifold+learning

...

Naver:"manifold learning"

Google:"manifold learning"

YouTube:"manifold learning"

"manifold learning"

manifold+learning

}

= MKLINK =

[[differential_geometry]]

[[symplectic_geometry]] =,symplectic_geometry =,symplectic_geometry . symplectic_geometry
{
WtEn:symplectic_geometry

@@ -145,18 +154,47 @@

rel
[[위상,topology]] [[위상수학,topology]]

= 같은 한국어 단어, 다른 영어 단어: =

== the Manifold Atlas Project ==

Manifold Atlas

http://www.map.mpim-bonn.mpg.de/Main_Page

= 같은단어 =

== 같은 한국어 단어, 다른 영어 단어: ==

[[다양체,variety]]

== manifold ==

see [[매니폴드,manifold]]

= Twins: =
https://artofproblemsolving.com/wiki/index.php/Manifold
https://mathworld.wolfram.com/Manifold.html

WpSp:Manifold

[[WpSp:Manifold]] = https://simple.wikipedia.org/wiki/Manifold

[[WpEn:Manifold]] = https://en.wikipedia.org/wiki/Manifold
https://www.proofwiki.org/wiki/Definition:Manifold

Namu:다양체

[[Namu:다양체]] = https://namu.wiki/w/다양체

...
Ndict:다양체 (한글검색결과에선 [[다양체,variety]] 내용을 구분할 것..)
Ndict:manifold

Naver:다양체+manifold

Bing:다양체+manifold

Ggl:다양체+manifold

YouTube:다양체+manifold

----

cp from local at [[Date(2023-09-24T19:58:36)]]

[[WpKo:다양체]] = https://ko.wikipedia.org/wiki/다양체

[[WpSp:Manifold]] = https://simple.wikipedia.org/wiki/Manifold

[[WpEn:Manifold]]

https://mathworld.wolfram.com/Manifold.html

https://ncatlab.org/nlab/show/manifold

https://encyclopediaofmath.org/wiki/Manifold

[[Libre:다양체]] = https://librewiki.net/wiki/다양체 //// 2022-2 현재토막글 / 2023-09 현재도

https://everything2.com/title/manifold

https://planetmath.org/manifold

----

1. Sub

1.1. topological m.

1.2. differentiable m. = smooth m.

1.3. complex m.

1.3.1. almost complex m.

1.4. symplectic m.

1.5. smooth m. / differentiable m. (DUPLICATED; 저위로 MERGE)

3.1. The Bright Side of Mathematics (YouTube)

3.1.1. 1

3.2. the Manifold Atlas Project

4. 같은단어

4.1. 같은 한국어 단어, 다른 영어 단어:
4.2. manifold

5. Twins:

[edit]

1. Sub ¶

[edit]

1.1. topological m. ¶

위상다양체 topological_manifold

topological_manifold
https://mathworld.wolfram.com/TopologicalManifold.html
https://www.proofwiki.org/wiki/Definition:Topological_Manifold

topological_manifold jjjjjjjjjjj

Topological_manifold = https://en.wikipedia.org/wiki/Topological_manifold
https://ncatlab.org/nlab/show/topological manifold
...

topological manifold

topological manifold
topological+manifold

[edit]

1.2. differentiable m. = smooth m. ¶

미분다양체 differentiable_manifold = 매끄러운다양체 smooth_manifold

https://mathworld.wolfram.com/SmoothManifold.html
https://freshrimpsushi.github.io/posts/differentiable-manifold/
...

미분다양체

매끄러운다양체

[edit]

1.3. complex m. ¶

복소다양체 complex_manifold
complex_manifold =,complex_manifold =,complex_manifold . complex_manifold

complex_manifold

MKLINK: complex_structure { https://ncatlab.org/nlab/show/complex structure }

복소다양체

= https://ko.wikipedia.org/wiki/복소다양체

complex_manifold eeeeeeeeeeee

Complex_manifold

= https://en.wikipedia.org/wiki/Complex_manifold

https://www.proofwiki.org/wiki/Definition:Topological_Manifold/Complex_Manifold

[edit]

1.3.1. almost complex m. ¶

almost complex manifold
almost_complex_manifold

MKLINK: almost_complex_structure or almost-complex_structure { https://encyclopediaofmath.org/wiki/Almost-complex_structure }
https://ko.wikipedia.org/wiki/개복소다양체
https://en.wikipedia.org/wiki/Almost_complex_manifold
Up: 매끄러운다양체

[edit]

1.4. symplectic m. ¶

(tmp)

symplectic

symplectic
symplectic =,symplectic .
사교다양체 symplectic_manifold
symplectic_manifold =,symplectic_manifold =,symplectic_manifold . symplectic_manifold

symplectic_manifold

심플렉틱 다양체, 사교다양체
MKLINK: symplectic_structure symplectic_form
https://encyclopediaofmath.org/wiki/Symplectic_manifold
https://mathworld.wolfram.com/SymplecticManifold.html

심플렉틱_다양체
https://ncatlab.org/nlab/show/symplectic manifold

MKL
symplectic_geometry

[edit]

1.5. smooth m. / differentiable m. (DUPLICATED; 저위로 MERGE) ¶

매끄러운다양체 smooth_manifold

매끄러운_다양체
https://mathworld.wolfram.com/SmoothManifold.html
https://www.proofwiki.org/wiki/Definition:Topological_Manifold/Smooth_Manifold
https://ncatlab.org/nlab/show/smooth manifold
매끄러움,smoothness

미분가능다양체 differentiable_manifold =,differentiable_manifold =,differentiable_manifold . differentiable_manifold

differentiable_manifold
https://www.proofwiki.org/wiki/Definition:Differentiable_Manifold

differentiable_manifold gggggg

Differentiable_manifold = https://en.wikipedia.org/wiki/Differentiable_manifold
미분가능성,differentiability

[edit]

1.6. Kähler m. ¶

Kähler

Kähler_manifold

ä = https://ko.wiktionary.org/wiki/ä

ä
https://ko.wikipedia.org/wiki/움라우트 - 그럼 ae로 표현?

Kahler_manifold or
Kaehler_manifold - pagename TBD.

ä transliteration

ä 표기

Kähler_manifold

= https://en.wikipedia.org/wiki/Kähler_manifold

[edit]

1.7. m. learning ¶

다양체학습? 학습,learning
manifold_learning =,manifold_learning =,manifold_learning . manifold_learning
{

manifold_learning

manifold_learning eeeeeee

manifold_learning ffffffff

...

manifold learning

manifold learning
"manifold learning"
manifold+learning
}

[edit]

2. MKLINK ¶

differential_geometry
symplectic_geometry =,symplectic_geometry =,symplectic_geometry . symplectic_geometry
{

symplectic_geometry

symplectic_geometry iiiiii
https://en.wikipedia.org/wiki/Symplectic_geometry
}
단위원판,unit_disk =단위원판,unit_disk =,unit_disk 단위원판 unit_disk
{

unit_disk

Unit_disk

Unit_disk = https://en.wikipedia.org/wiki/Unit_disk

단위,unit 원판,disk
...

단위원판

단위원판
}
열린단위원판,open_unit_disk =열린단위원판,open_unit_disk =,open_unit_disk 열린단위원판 open_unit_disk
{

open_unit_disk

열린단위원판

열린단위원판
}

manifold는 shape의 일반화,generalization?
shape에 대한 페이지를 만들어야 하는데... or figure?
모양,shape or 도형,shape or 도형,geometric_shape - 도형이 좀더 기하적인 용어
{

도형
}

다양체,manifold 개념,concept은
곡면,surface이나 공간,space 개념의 일반화,generalization? [1]

[edit]

3. Bmks ¶

[edit]

3.1. The Bright Side of Mathematics (YouTube) ¶

https://www.youtube.com/@brightsideofmaths

Manifolds (Playlist)
https://www.youtube.com/playlist?list=PLBh2i93oe2qvRGAtgkTszX7szZDVd6jh1
2023-09-13 현재 Part 20까지 있고 '사용할 수 없는 동영상 5개가 숨겨졌습니다.' + 마지막 Part 20만 dark version 있음, 8일 전. - dark version 만드는 중?

[edit]