From 32791298bc151ad8702596fd3a8bed368388f677 Mon Sep 17 00:00:00 2001 From: oskar Date: Mon, 30 Mar 2026 02:37:14 +0200 Subject: [PATCH] device-56.home 2026-3-30:2:37:13 --- .../Drawing 2026-03-30 01.05.52.excalidraw.md | 179 ----------------- ...Drawing 2026-03-30 01.05.52.excalidraw.svg | 2 - .../demo_théorème_du_début_2.excalidraw.md | 183 ++++++++++++++++++ .../demo_théorème_du_début_2.excalidraw.svg | 2 + ...ur non spécialistes – suite look-and-say.md | 25 ++- attachments/Pasted image 20260330021624.png | Bin 0 -> 20555 bytes désintégration audioactive.md | 21 +- 7 files changed, 227 insertions(+), 185 deletions(-) delete mode 100644 Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.md delete mode 100644 Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.svg create mode 100644 Excalidraw/demo_théorème_du_début_2.excalidraw.md create mode 100644 Excalidraw/demo_théorème_du_début_2.excalidraw.svg create mode 100644 attachments/Pasted image 20260330021624.png diff --git a/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.md b/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.md deleted file mode 100644 index 0eb1a1ac..00000000 --- a/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.md +++ /dev/null @@ -1,179 +0,0 @@ ---- - -excalidraw-plugin: parsed -tags: [excalidraw] - ---- -==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' - - -# Excalidraw Data - -## Text Elements -## Embedded Files -0c2ad4dae5ed514b2fd2099d68d0760c69fbce4d: $$[1^{1}]$$ - -f9c478059e1cce4e96a58e13baac6bfbb4f93eff: $$[1^{1}X^{1}$$ - -214cc7890168fcc3649c7581bd637e267a6de7bf: $$[1^{1}2^{2}$$ - -84fa363149df51fc341b5998c6b4e67ed3dbdb8e: $$[1^{3}$$ - -f49bf0b1178f855291cee484fe1921917621c6c0: $$[1^{1}3^{2}$$ - -c6ae105adef2251de3956c588d95fb1ed29d572b: $$[1^{2}2^{2}$$ - -f7ab87077d1c10f7309f5bbce5c714d5f25bef0f: $$[1^{2}2^{3}$$ - -539b82e2e9bc43b1e2665050071a453e72116434: $$[2^{1}X^{2}$$ - -082b26651855e6e47f735b3481c3b45c1678ff69: $$2^{1}X^{\neq 2}$$ - -76483ecab4b1eb14f16fcd978d387e8ac0f6344a: $$[2^{3}$$ - -32a8965b6d15d90d3898edfdb7969dbd9a92f3c8: $$[3^{1}X^{3}$$ - -cc5e37cfba585550da4471dd85852d6a38354787: $$[3^{1}X^{\leq 2}$$ - -b752624b6df8d46597c3242c793dafa003ae9422: $$[3^{2}X^{3}$$ - -848fe42b60268d03c05e522d05a9dd988119d57b: $$[3^{2}X^{\leq 2}$$ - -98ffd4aa77ffc7c0ea17203a781a2cd621186d8e: $$[n^{1}$$ - -8aef2acc0c00b47668a81c160807e1ab6d4b03ce: $$[1^{2}X^{1}$$ - -%% -## Drawing -```compressed-json -N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebR4ARniaOiCEfQQOKGZuAG1wMFAwYogSbggOAAVSYgBBAEkAdmajODY2AE4E/AAzbAAGADUAKRTiyFhEcsJ9aKR+EsxuZwBm - -ABZ+7Q7GgDYAVh41vZWADh2ebYXIGGWEjp3tHcaEk73z/p4dnY+9q4gKEjqbh7NbaZ4rHYJNbgjofT5/SQIQjKaTcNZJforA4JBKYkGfRp/azKYLcfp/ZhQUhsADWCAAwmx8GxSOUAMT9TlcsYlTS4bA05TUoQcYiM5msiRU6zMOC4QJZHmQHqEfD4ADKsFJEkk/I0gSVEEp1LpAHVAZJuAkKVTaQhNTBtehBB5DcKURxwjk0NaCpA2HLsGobj7O - -X9haLPcxvagOEI1RSEAhiFa1icIXszoS/QwmKxONwsXwc4wWOwOAA5ThiK0JfYrdbpv5CODEXBQZNW5ppngnLpfHYdP6EZgAETSHZTaB6BDCfyFwjg9WIMdyAF0/pphKKAKLBDJZVcbnNEDg07hxhMntgCzvT2cIP49cgZZcX+P4BGhAAqWCgABlCDPbgZ3wOccxVYI3wkfpsB4XBiDWNsED2ZM9ihTQeB6YgeH6DoOmIHYTmIfpdlgwcek0MQkM - -NbAhEpAxR3bXBuCKcYIHwdssHKXIEgAPWABIAF81wgP0hIpdxxFQfJxjAX05ISP1j3YoDiG4iRcH6Q1KXbejykQUUgOUWjqTgd81QKCSCjYyAygkao1gAeScvSAEd9GIAAxZQ1g6GkAE1vzgTBTUNSZpNKWZlHmHMljQNNHkxfodjWBtEjwoi/hDVBnEabRXk+dMdlOF49n6N4/gBYggTQDoVm0NZBzwl4Pn7FZs3YxFkVRBKMSLHE8TWAkiQ4El - 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-NUmQEIAZK3IlPLVA+8EwCZAWOEjI1+h3iODfKa/rX5deI4BqgkAJUov64A9XsZAIBFGggDgApsK5wxgwAKXBCQQAA=== -``` -%% \ No newline at end of file diff --git a/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.svg b/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.svg deleted file mode 100644 index ddfefd1f..00000000 --- a/Excalidraw/Drawing 2026-03-30 01.05.52.excalidraw.svg +++ /dev/null @@ -1,2 +0,0 @@ - \ No newline at end of file diff --git a/Excalidraw/demo_théorème_du_début_2.excalidraw.md b/Excalidraw/demo_théorème_du_début_2.excalidraw.md new file mode 100644 index 00000000..fd26bb98 --- /dev/null +++ b/Excalidraw/demo_théorème_du_début_2.excalidraw.md @@ -0,0 +1,183 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' + + +# Excalidraw Data + +## Text Elements +## Embedded Files +0c2ad4dae5ed514b2fd2099d68d0760c69fbce4d: $$[1^{1}]$$ + +f9c478059e1cce4e96a58e13baac6bfbb4f93eff: $$[1^{1}X^{1}$$ + +214cc7890168fcc3649c7581bd637e267a6de7bf: $$[1^{1}2^{2}$$ + +84fa363149df51fc341b5998c6b4e67ed3dbdb8e: $$[1^{3}$$ + +f49bf0b1178f855291cee484fe1921917621c6c0: $$[1^{1}3^{2}$$ + +539b82e2e9bc43b1e2665050071a453e72116434: $$[2^{1}X^{2}$$ + +082b26651855e6e47f735b3481c3b45c1678ff69: $$2^{1}X^{\neq 2}$$ + +76483ecab4b1eb14f16fcd978d387e8ac0f6344a: $$[2^{3}$$ + +32a8965b6d15d90d3898edfdb7969dbd9a92f3c8: $$[3^{1}X^{3}$$ + +cc5e37cfba585550da4471dd85852d6a38354787: $$[3^{1}X^{\leq 2}$$ + +b752624b6df8d46597c3242c793dafa003ae9422: $$[3^{2}X^{3}$$ + +848fe42b60268d03c05e522d05a9dd988119d57b: $$[3^{2}X^{\leq 2}$$ + +98ffd4aa77ffc7c0ea17203a781a2cd621186d8e: $$[n^{1}$$ + +8aef2acc0c00b47668a81c160807e1ab6d4b03ce: $$[1^{2}X^{1}$$ + +f297bb8c586c081e6495ec2b90fc2134c5756fa0: $$[1^{2}X^{\neq 1}$$ + +%% +## Drawing +```compressed-json +N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebR4ARniaOiCEfQQOKGZuAG1wMFAwYogSbggOAAVSYgBBAEkAdmajODY2AE4E/AAzbAAGADUAKRTiyFhEcsJ9aKR+EsxuZwAW + +AGY4gDYVgA4OjoBWBJXN/o6eA4XIGGWdne01g93+nd3NhM2DzauIChJ1bhPbSNBJrd4rEFrDr9Hg8b4FSCSBCEZTSbgrJL9R6JBJYp5wxo/azKYLcfo/ZhQUhsADWCAAwmx8GxSOUAMT9TlcsYlTS4bA05TUoQcYiM5msiRU6zMOC4QJZHmQHqEfD4ADKsFJEkk/I0gSVEEp1LpAHV/pJuAkKVTaQhNTBtehBB5DcLURxwjk0NaERA2HLsGobj7O + +T9haLPcxvagOEI1RSEAhiFbdmCDjtNoS/YwWOwuGgDv0Vj9c6xOAA5ThibiNE47I4rLE/IRwYi4KDJq3NXY8DqbNYvEE/QjMAAiaU7KbQPQIYR+QuEcHqxBjuQAuj9NMJRQBRYIZLJrhGFE+QMoSU2YGD0AAyBwA4rUlSVJuJ0PLqVQTwBfBGbv0iA4GluDjBNALYAUuxnOcEB+HpyAyFdQPjfAfl1ZgABUsCgW9CGA7hZ3wec/RVYJkIkfpsB4X + 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+9rJC/AqCExIBmwAiALnjX9/yS/x98UYIQCgAgId8DX9ZgUgDpBSACsFhxTtIBjuCHg8oNnN9gxILsAq4BAmyB1Qf8jgBSgplA+DKgxwWQRsAFYMYBMIdoEcUSEAMjCBggSELaQmTAwEMDGMRtRY8R4AwF/wkQlYK3Jm1NSEpBagZEOhDYQ4fQ/9HAZgD2DGQLIBwgTUTICEBwQyPC+Zqge+CYBMge9Bwc9gwGj/RdRUEP2Cb/UcBNQSATEQBC4nO + +AB8gBQ0xQQBwAH2Hk1wgJSD/AfwIAA== +``` +%% \ No newline at end of file diff --git a/Excalidraw/demo_théorème_du_début_2.excalidraw.svg b/Excalidraw/demo_théorème_du_début_2.excalidraw.svg new file mode 100644 index 00000000..ed7b428f --- /dev/null +++ b/Excalidraw/demo_théorème_du_début_2.excalidraw.svg @@ -0,0 +1,2 @@ + \ No newline at end of file diff --git a/Mathématiques pour non spécialistes – suite look-and-say.md b/Mathématiques pour non spécialistes – suite look-and-say.md index afe7581c..94182391 100644 --- a/Mathématiques pour non spécialistes – suite look-and-say.md +++ b/Mathématiques pour non spécialistes – suite look-and-say.md @@ -114,5 +114,28 @@ Le début arrivera toujours sur l'un de ces cycles : ### Théorème du début — Démonstration 3) Simplifier les cas (en assimiler certains) +![[attachments/Pasted image 20260330021624.png]] +La version de Conway : -![[attachments/Capture d’écran 2026-03-29 à 22.50.04.png]] \ No newline at end of file +![[attachments/Capture d’écran 2026-03-29 à 22.50.04.png]] + + +--- +## Théorème du découpage + +> [!definition] Découpage +> Quand les descendants de $L$ et $R$ n'interfèrent jamais dans $LR$, c'est-à-dire : +> $\forall n,\quad (LR)_{n} = L_{n}R_{n}$ +> +> On dit que $LR$ se **découpe** en $L \cdot R$ + + +-- +## Théorème du découpage + + +> [!definition] Découpage trivial +> $[\;\;]\cdot R$ ou $L \cdot [\;\;]$ + +> [!definition] Atome +> - **atome** : morceau sans découpage non trivial diff --git a/attachments/Pasted image 20260330021624.png b/attachments/Pasted image 20260330021624.png new file mode 100644 index 0000000000000000000000000000000000000000..a32471d7ad409c93c230726c63b01a796685518a GIT binary patch literal 20555 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M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=181&selection=221,11,241,7&color=note|(John Horton Conway, 1987)]] +^def-atome - i toute chaîne est **composée** d'un certain nombre d'éléments. On dit que cette chaîne **comprends** lesdits éléments. - source:: [[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=181&selection=243,5,260,9&color=note|(John Horton Conway, 1987)]] @@ -211,7 +213,7 @@ header-auto-numbering: > > - en assimilant $[3^{1}X^{1}$ et $[3^{1}(\leq 2)^{2}$ aux deux cas $[3^{1}X^{3}$, $[3^{1}X^{\leq 2}$ > > - en assimilant $[3^{2}(\leq 2)^{\leq 3}$ aux cas $[3^{2}X^{3}$, $[3^{2}X^{\leq 2}$ > > - en assimilant $[1^{3}2^{2}$ et $[1^{3}X^{1}$ au seul cas $[1^{3}$ -> > - en séparant $[1^{2}2^{\leq 3}$ en $[1^{2}X^{1}$ (qui est déjà listé), $[1^{2}2^{2}$, $[1^{2}2^{3}$ +> > - en assimilant $[1^{2}2^{\leq 3}$ à $[1^{2}X^{1}$ (qui est déjà listé) et $[1^{2}X^{\neq 1}$ > > - en séparant $[2^{1} X^{\leq 2}$ en $[2^{1}X^{2}$ et $[2^{1}X^{\neq 2}$ > > - en ajoutant $[1^{1}3^{2}$ > > Cela nous donne la liste suivante : @@ -220,8 +222,7 @@ header-auto-numbering: > > - $[1^{2}X^{1}$ > > - $[1^{1}2^{2}$ > > - $[1^{1}3^{2}$ -> > - $[1^{2}2^{2}$ -> > - $[1^{2}2^{3}$ +> > - $[1^{2}X^{\neq 1}$ > > - $[1^{3}$ > > - $[2^{1}X^{2}$ > > - $[2^{1}X^{\neq 2}$ @@ -234,7 +235,21 @@ header-auto-numbering: > > > > Cela nous permet d'atteindre le schéma original de Conway : > > ![[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=186&rect=12,345,377,408|schéma original de Conway p.186]] +^theoreme-debut +> [!proposition]+ théorème du découpage +> Un chaîne de $\geq 2$ jour $LR$ se découpe en $L \cdot R$ seulement dans ces cas : +> +> | L | R | +> | --------- | --------------------------------------------------------------------------------------------- | +> | $n]$ | $[m$ | +> | $2]$ | $[1^1X^1$ ou $[1^{3}$ ou $[3^{1}X^{\neq 3}$ ou $[n^{1}$ | +> | $\neq 2]$ | $[2^{2} 1^{1}X^{1}$ ou $[2^{2}1^{3}$ ou $[2^{2}3^{1}X\neq 3$ ou $[2^{2}n^{(0 \text{ ou } 1)}$ | +> avec $n \geq 4$ et $m \leq 3$ +> ou bien quand l'un des deux est vide ($L = [\;\;]$ ou $R = [\;\;]$) +> > [!démonstration]- Démonstration +> > Cela suit directement du [[désintégration audioactive#^theoreme-debut|téorème du début]] appliqué à $R$, et du fait que le dernier chiffre de $L$ est constant + ^theoreme-decoupage ## Tableau des éléments