From 654decd27f98e076ed2683c8909f62ea0e33ef32 Mon Sep 17 00:00:00 2001 From: oskar Date: Thu, 16 Apr 2026 15:55:33 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-16:15:55:33 --- .../obsidian-excalidraw-plugin/data.json | 2 +- ...aux bords arrondis 2026-04-16.excalidraw.md | 154 ++++++++++++++++++ ...ux bords arrondis 2026-04-16.excalidraw.svg | 2 + 3 files changed, 157 insertions(+), 1 deletion(-) create mode 100644 Excalidraw/problème de la plus grande diagonale d'une valise aux bords arrondis 2026-04-16.excalidraw.md create mode 100644 Excalidraw/problème de la plus grande diagonale d'une valise aux bords arrondis 2026-04-16.excalidraw.svg diff --git a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json index df63189c..cec0b847 100644 --- a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json +++ b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json @@ -113,7 +113,7 @@ "library2": { "type": "excalidrawlib", "version": 2, - "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.21.2", + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.22.0", "libraryItems": [] }, "imageElementNotice": true, diff --git a/Excalidraw/problème de la plus grande diagonale d'une valise aux bords arrondis 2026-04-16.excalidraw.md b/Excalidraw/problème de la plus grande diagonale d'une valise aux bords arrondis 2026-04-16.excalidraw.md new file mode 100644 index 00000000..824a4c0a --- /dev/null +++ b/Excalidraw/problème de la plus grande diagonale d'une valise aux bords arrondis 2026-04-16.excalidraw.md @@ -0,0 +1,154 @@ +--- + +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 +le tableau de variations est évident étant donné le problème considéré. +On pourra toujours montrer que cet unique extrémum est bien un maximum à partir du fait que 𝑎 ∈ [0; π/2] ^OnHRRJcd + +## Embedded Files +8923efd922b888d467179262d7b788641d043cc7: $$l$$ + +b3d5701da7f512bb6c2cfeefa687ef9448961a27: $$L$$ + +a745f1dc9892805697eb7dc6df5134ce60d3e778: $$\alpha$$ + +b76ee720d7e0bdf63f408ee39db94f3d31ca9f0e: $$r$$ + +13099823a77cd5a2252736e0f029c959c6ee8e2c: $$=\begin{pmatrix}l\\L\end{pmatrix}$$ + +e8b51e7e123fde3009046ff7524c05292519716e: $$=\begin{pmatrix}r \cos \alpha\\ r \sin \alpha\end{pmatrix}$$ + +2eb73fd7a8bd07b84080b3bb149f4819930587be: $$= \begin{pmatrix}l + r \cos \alpha\\ L + r \sin \alpha\end{pmatrix}$$ + +4dd7657e8aff3434304e0c34035d8f6e3e9c7c5d: $$\text{donc :}$$ + +ce7a3ec53f89ae18583ec0042233662e411ba23b: $$\begin{align} \left\| \begin{pmatrix}l+r\cos \alpha\\L+r \sin \alpha\end{pmatrix} \right\| &= l^{2}+2lr\cos\alpha + r^{2}\cos ^{2}\alpha + L^{2} + 2Lr\sin\alpha + r^{2}\sin ^{2}\alpha \\&= (l^{2}+L^{2}+r^{2}) + 2r(l\cos\alpha+L\sin\alpha)\end{align}$$ + +16647f064fb7a498cb3e96cfa483672e387b3557: $$\text{on veut donc maximiser } f: f(\alpha) = l\cos\alpha+L\sin\alpha$$ + +c07e13d38824e5b0021dd5fdfadb2c55ad79c69a: $$f'(\alpha) = -l\sin\alpha + L\cos\alpha$$ + +fafa660ca9b7e22e4de89da24218f9436103d840: $$\begin{align} f'(\alpha) = 0 &\iff L \cos \alpha = l \sin \alpha \\&\iff \frac{L}{l} \frac{\cos \alpha}{\sin\alpha} = 1 \\&\iff \tan \alpha = \frac{l}{L} \\&\iff \boxed {\alpha = \arctan \frac{l}{L}} \end{align}$$ + +%% +## Drawing +```compressed-json +N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebR44gAYaOiCEfQQOKGZuAG1wMFAwYogSbggAdQ4AdgAzACkALQ4AQQBFAGkhCgAlABUe6raEAFYoADYU4shYRHKiDiR+Esxu + 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2026-04-16.excalidraw.svg @@ -0,0 +1,2 @@ +le tableau de variations est évident étant donné leproblème considéré.On pourra toujours montrer que cet uniqueextrémum est bien un maximum à partir du fait que𝑎 ∈ [0; π/2] \ No newline at end of file