From 7d4f9bfae50fb9253c9a185daef89bc61165da4e Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Thu, 12 Oct 2023 11:48:44 +0200 Subject: [PATCH] vault backup: 2023-10-12 11:48:44 --- .../obsidian-activity-history/data.json | 4 +- .../various-complements/histories.json | 2 +- notes/.obsidian/workspace.json | 22 +++++----- notes/mat/Geometrie/Geometrie.md | 1 + notes/mat/Geometrie/Kružnice.md | 42 +++++++++++++++++++ 5 files changed, 57 insertions(+), 14 deletions(-) create mode 100644 notes/mat/Geometrie/Kružnice.md diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index 3d09b15..caaf3b1 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -13,7 +13,7 @@ { "path": "/", "date": "2023-10-12", - "size": 1447287 + "size": 1448320 } ], "activityHistory": [ @@ -1358,7 +1358,7 @@ }, { "date": "2023-10-12", - "value": 1234 + "value": 2267 } ] } diff --git a/notes/.obsidian/plugins/various-complements/histories.json b/notes/.obsidian/plugins/various-complements/histories.json index c16cab9..b44669a 100644 --- a/notes/.obsidian/plugins/various-complements/histories.json +++ b/notes/.obsidian/plugins/various-complements/histories.json @@ -1 +1 @@ -{"\\sphericalangle":{"\\sphericalangle":{"currentFile":{"count":1,"lastUpdated":1694680712479}}},"Logaritmus":{"Logaritmus":{"internalLink":{"count":1,"lastUpdated":1694690308884}}},"zobrazení":{"zobrazení":{"currentFile":{"count":2,"lastUpdated":1694769120832}}},"Druhý pohybový zákon":{"Druhý pohybový zákon":{"internalLink":{"count":1,"lastUpdated":1695281570945}}},"\\sin\\alpha":{"\\sin\\alpha":{"currentFile":{"count":1,"lastUpdated":1695293974762}}},"\\frac{1.33}{\\frac{\\sqrt2}1}":{"\\frac{1.33}{\\frac{\\sqrt2}1}":{"currentFile":{"count":1,"lastUpdated":1695297376494}}},"\\frac{\\sin60\\degree\\cos\\alpha-\\cos60\\degree\\sin\\alpha}{\\sin\\alpha}":{"\\frac{\\sin60\\degree\\cos\\alpha-\\cos60\\degree\\sin\\alpha}{\\sin\\alpha}":{"currentFile":{"count":1,"lastUpdated":1695298838520}}},"individuální":{"individuální":{"currentFile":{"count":2,"lastUpdated":1697092098229}}},"psychická":{"psychická":{"currentFile":{"count":1,"lastUpdated":1697092095287}}},"Statky":{"Statky":{"currentFile":{"count":1,"lastUpdated":1697095385570}}},"Politika první republiky":{"Politika první republiky":{"internalLink":{"count":1,"lastUpdated":1697095390438}}},"uspokojuje":{"uspokojuje":{"currentFile":{"count":1,"lastUpdated":1697095392504}}},"Osobnosti":{"Osobnosti":{"internalLink":{"count":1,"lastUpdated":1697096048794}}}} \ No newline at end of file +{"\\sphericalangle":{"\\sphericalangle":{"currentFile":{"count":2,"lastUpdated":1697099285538}}},"Logaritmus":{"Logaritmus":{"internalLink":{"count":1,"lastUpdated":1694690308884}}},"zobrazení":{"zobrazení":{"currentFile":{"count":2,"lastUpdated":1694769120832}}},"Druhý pohybový zákon":{"Druhý pohybový zákon":{"internalLink":{"count":1,"lastUpdated":1695281570945}}},"\\sin\\alpha":{"\\sin\\alpha":{"currentFile":{"count":1,"lastUpdated":1695293974762}}},"\\frac{1.33}{\\frac{\\sqrt2}1}":{"\\frac{1.33}{\\frac{\\sqrt2}1}":{"currentFile":{"count":1,"lastUpdated":1695297376494}}},"\\frac{\\sin60\\degree\\cos\\alpha-\\cos60\\degree\\sin\\alpha}{\\sin\\alpha}":{"\\frac{\\sin60\\degree\\cos\\alpha-\\cos60\\degree\\sin\\alpha}{\\sin\\alpha}":{"currentFile":{"count":1,"lastUpdated":1695298838520}}},"individuální":{"individuální":{"currentFile":{"count":2,"lastUpdated":1697092098229}}},"psychická":{"psychická":{"currentFile":{"count":1,"lastUpdated":1697092095287}}},"Statky":{"Statky":{"currentFile":{"count":1,"lastUpdated":1697095385570}}},"Politika první republiky":{"Politika první republiky":{"internalLink":{"count":1,"lastUpdated":1697095390438}}},"uspokojuje":{"uspokojuje":{"currentFile":{"count":1,"lastUpdated":1697095392504}}},"Osobnosti":{"Osobnosti":{"internalLink":{"count":1,"lastUpdated":1697096048794}}},"Kružnice":{"Kružnice":{"currentFile":{"count":1,"lastUpdated":1697098733268}}}} \ No newline at end of file diff --git a/notes/.obsidian/workspace.json b/notes/.obsidian/workspace.json index f9c3243..37a9493 100644 --- a/notes/.obsidian/workspace.json +++ b/notes/.obsidian/workspace.json @@ -4,16 +4,16 @@ "type": "split", "children": [ { - "id": "48fc1f277ebb4b13", + "id": "c3998d360a5b7415", "type": "tabs", "children": [ { - "id": "12826dc958d28015", + "id": "d8cc7361e60e9cfb", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "eko/Úvodní hodina.md", + "file": "mat/Geometrie/Kružnice.md", "mode": "source", "source": false } @@ -85,7 +85,7 @@ "state": { "type": "backlink", "state": { - "file": "eko/Úvodní hodina.md", + "file": "mat/Geometrie/Kružnice.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -102,7 +102,7 @@ "state": { "type": "outgoing-link", "state": { - "file": "eko/Úvodní hodina.md", + "file": "mat/Geometrie/Kružnice.md", "linksCollapsed": false, "unlinkedCollapsed": true } @@ -149,7 +149,7 @@ "state": { "type": "outline", "state": { - "file": "eko/Úvodní hodina.md" + "file": "mat/Geometrie/Kružnice.md" } } }, @@ -235,9 +235,13 @@ "breadcrumbs:Breadcrumbs Visualisation": false } }, - "active": "12826dc958d28015", + "active": "d8cc7361e60e9cfb", "lastOpenFiles": [ + "mat/Funkce/Příklady.md", + "mat/Geometrie/Kružnice.md", + "mat/mat.md", "eko/eko.md", + "eko/Úvodní hodina.md", "data/Uplny odraz svetla 2023-09-21 12.58.19.excalidraw.md", "fyz/Svetlo/Odraz světla.md", "data/Odraz světla 2023-09-21 14.11.58.excalidraw.md", @@ -247,9 +251,7 @@ "mat/Funkce/Sinus.md", "data/Uplny odraz svetla 2023-09-21 12.52.08.excalidraw.md", "fyz/fyz.md", - "mat/mat.md", "kbb/math/Modulární aritmetika.md", - "eko/Úvodní hodina.md", "eko/Untitled.md", "mat/Geometrie/Geometrie.md", "mat/Geometrie/Konstrukční úlohy.md", @@ -264,9 +266,7 @@ "mat/Geometrie", "cjl/cjl.md", "data/Odraz světla 2023-09-14 13.19.17.excalidraw.md", - "fyz/Svetlo/Svetlo.md", "fyz/Svetlo", - "mat/Ekvigonala.md", "PRA", "Maturitni cetba", "projects/dvop", diff --git a/notes/mat/Geometrie/Geometrie.md b/notes/mat/Geometrie/Geometrie.md index 01c8168..ea70211 100644 --- a/notes/mat/Geometrie/Geometrie.md +++ b/notes/mat/Geometrie/Geometrie.md @@ -1,6 +1,7 @@ # Geometrie %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[mat/Geometrie/Konstrukční úlohy|Konstrukční úlohy]] +- [[mat/Geometrie/Kružnice|Kružnice]] - [[mat/Geometrie/Středová souměrnost|Středová souměrnost]] - [[mat/Geometrie/Zobrazení v rovině|Zobrazení v rovině]] %% Zoottelkeeper: End of the autogenerated index file list %% diff --git a/notes/mat/Geometrie/Kružnice.md b/notes/mat/Geometrie/Kružnice.md new file mode 100644 index 0000000..1a21913 --- /dev/null +++ b/notes/mat/Geometrie/Kružnice.md @@ -0,0 +1,42 @@ +# Kružnice + +## Oblouk + +$k; k(S; ?)$ +$\stackrel{\smallfrown}{AB}; \stackrel{\smallfrown}{AB} \in k$ +$\sphericalangle ASB; \stackrel{\smallfrown}{AB} \in \sphericalangle ASB$ + +středový úhel ($\sphericalangle ASB$) přísluší oblouku $\stackrel{\smallfrown}{AB}$ tak, aby v něm oblouk ležel. + +$V; V\in k; V\not\in\stackrel{\smallfrown}{AB}$ +$\sphericalangle AVB$ + +Obvodový úhel ($\sphericalangle AVB$) je takový, že v něm $\stackrel{\smallfrown}{AB}$ leží. + +> [!SENTENCE] +> Velikost středového úhlu příslušného $\stackrel{\smallfrown}{AB}$ je rovna dvojnásobku obvodového úhlu příslušného témuž oblouku. + +i.e. $|\sphericalangle AVB|=\frac{|\sphericalangle ASB|}2$ + + + +### Tětivový čtyřúhelník + +Čtyřúhelník postaven z tětiv. + +Platí že $\alpha+\delta=180\degree=\gamma+\beta$ + + + + + + + + + + + + +$$\frac{\sin\alpha}{\sin60\cos\alpha-\cos60\sin\alpha}|/\sin\alpha$$ +$$\frac{1}{\sin60\frac{\cos\alpha}{\sin\alpha}-\cos60}$$ +$$\frac{1}{\sin60\cotg\alpha-\cos60}$$