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Daniel Bulant 2024-02-16 12:35:35 +01:00
parent 866788be50
commit 03f3681dc0
18 changed files with 15752 additions and 488 deletions
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10
notes/.obsidian/plugins/obsidian-activity-history/data.json vendored
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35
notes/.obsidian/workspace.json vendored
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---
excalidraw-plugin: parsed
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
vnitřní dotyk ^3JTfbLDS
vnější dotyk ^uyD0vOPu
%%
# Drawing
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```
%%

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
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# Drawing
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%%

190
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@ -0,0 +1,190 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
```json
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"version": 2,
"source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/1.9.27",
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"frameRendering": {
"enabled": true,
"clip": true,
"name": true,
"outline": true
}
},
"files": {}
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```
%%

8
notes/data/data.md
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@ -9,6 +9,10 @@ type: folder_brief_live
imagePrefix: 'data/'
```
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[data/2 kružnice 2024-02-16 12.14.40.excalidraw|2 kružnice 2024-02-16 12.14.40.excalidraw]]
- [[data/2 kružnice 2024-02-16 12.15.11.excalidraw.svg|2 kružnice 2024-02-16 12.15.11.excalidraw.svg]]
- [[data/2 kružnice 2024-02-16 12.15.11.excalidraw|2 kružnice 2024-02-16 12.15.11.excalidraw]]
- [[data/2 kružnice 2024-02-16 12.15.54.excalidraw|2 kružnice 2024-02-16 12.15.54.excalidraw]]
- [[data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw|Absolutní hodnota_2022-02-23 09.05.43.excalidraw]]
- [[data/akabus.png|akabus.png]]
- [[data/Analytická geometrie 2023-12-08 11.57.01.excalidraw|Analytická geometrie 2023-12-08 11.57.01.excalidraw]]
@ -51,6 +55,8 @@ imagePrefix: 'data/'
- [[data/kótování příklad 1.bmp|kótování příklad 1.bmp]]
- [[data/kótování příklad 1.svg|kótování příklad 1.svg]]
- [[data/Kružnice 2023-10-13 11.32.35.excalidraw|Kružnice 2023-10-13 11.32.35.excalidraw]]
- [[data/Kružnice 2024-02-15 11.29.46.excalidraw.svg|Kružnice 2024-02-15 11.29.46.excalidraw.svg]]
- [[data/Kružnice 2024-02-15 11.29.46.excalidraw|Kružnice 2024-02-15 11.29.46.excalidraw]]
- [[data/Kužolosečky 2024-02-15 10.22.05.excalidraw.svg|Kužolosečky 2024-02-15 10.22.05.excalidraw.svg]]
- [[data/Kužolosečky 2024-02-15 10.22.05.excalidraw|Kužolosečky 2024-02-15 10.22.05.excalidraw]]
- [[data/Kužolosečky 2024-02-15 10.22.28.excalidraw.svg|Kužolosečky 2024-02-15 10.22.28.excalidraw.svg]]
@ -61,6 +67,8 @@ imagePrefix: 'data/'
- [[data/Kužolosečky 2024-02-15 10.30.09.excalidraw|Kužolosečky 2024-02-15 10.30.09.excalidraw]]
- [[data/Kužolosečky 2024-02-15 10.43.44.excalidraw|Kužolosečky 2024-02-15 10.43.44.excalidraw]]
- [[data/Kužolosečky 2024-02-15 10.44.44.excalidraw|Kužolosečky 2024-02-15 10.44.44.excalidraw]]
- [[data/Kužolosečky 2024-02-15 11.00.14.excalidraw|Kužolosečky 2024-02-15 11.00.14.excalidraw]]
- [[data/Kužolosečky 2024-02-15 11.01.27.excalidraw|Kužolosečky 2024-02-15 11.01.27.excalidraw]]
- [[data/Matice 1.bmp|Matice 1.bmp]]
- [[data/Matice 2.bmp|Matice 2.bmp]]
- [[data/Matice 3.bmp|Matice 3.bmp]]

49
notes/mat/Geometrie/Analytická/2 kružnice.md Normal file
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@ -0,0 +1,49 @@
# 2 kružnice
1. všechny body společné = totožné
![[2 kružnice 2024-02-16 12.14.40.excalidraw]]
2. 2 společné body
![[2 kružnice 2024-02-16 12.15.11.excalidraw]]
3. 1 společný bod
![[2 kružnice 2024-02-16 12.15.54.excalidraw]]
---
Najděte společné body kružnic, mají-li nějaké:
$u: x^2+y^2-2y-4=0$
$v:x^2+y^2+4x-6=0$
$-2y-4x+2=0$
$y+2x-1=0$
$y=-2x+1$
$x^2-(2x+1)^2+4x-6=0$
$x^2+4x^2-4x+1+4x-6=0$
$5x^2-5=0$
$x^2-1=0$
$(x+1)(x-1)=0$
$x_1=-1$
$y_1=-2(-1)+1=3$
$x_2=1$
$y_2=-2*1+1=-1$
$R_1=[-1;3]$
$R_2=[1;-1]$
---
$x^2+y^2-2y-4=0$
$S=[0;1]$
$r=\sqrt5$
$(x-0)^2+(y-1)^2=5$
---
$x^2+y^2+4x-6=0$
$S=[-2;0]$
$r=\sqrt{10}$
$(x+2)^2+y^2=10$

4
notes/mat/Geometrie/Analytická/Analytická.md
View file

@ -1,7 +1,9 @@
# Analytická
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[mat/Geometrie/Analytická/2 kružnice|2 kružnice]]
- [[mat/Geometrie/Analytická/Jednotkový vektor|Jednotkový vektor]]
- [[mat/Geometrie/Analytická/Kužolosečky|Kužolosečky]]
- [[mat/Geometrie/Analytická/Kružnice|Kružnice]]
- [[mat/Geometrie/Analytická/Kuželosečky|Kuželosečky]]
- [[mat/Geometrie/Analytická/Nulový vektor|Nulový vektor]]
- [[mat/Geometrie/Analytická/Odchylka vektorů|Odchylka vektorů]]
- [[mat/Geometrie/Analytická/Orientovaná úsečka|Orientovaná úsečka]]

87
notes/mat/Geometrie/Analytická/Kružnice.md Normal file
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@ -0,0 +1,87 @@
# Kružnice
Množina bodů ($X$) v rovině, které mají od zadaného bodu ($S$) stejnou zadanou vzdálenost ($r$).
![[Kružnice 2024-02-15 11.29.46.excalidraw]]
$|XS|=r$
$S=[x_s;y_s]$
$X=[x;y]$
$r=\sqrt{(x-x_s)^2+(y-y_s)^2}$
> [!SENTENCE]
> $(x-x_s)^2+(y-y_s)^2=r^2$
> středová rovnice kružnice
$(x-x_s)^2+(y-y_s)^2=r^2$
$x^2-2xx_s+x_s^2+y^2-2yy_s+y_s^2-r^2=0$
$x^2-2x_sx+y^2-2y_sy+x_s^2+y_s^2-r^2=0$
$p=x_s^2+y_s^2-r^2$
> [!SENTENCE]
> $x^2-2x_sx+y^2-2y_sy+p=0$
> Obecná rovnice kružnice $k$
---
$k(S;r)$
$S=[\sqrt2;-1];r=\sqrt3$
$A=[2\sqrt2;0];A\in k$
$k:(x-\sqrt2)^2+(y+1)^2=3$
$x^2-2\sqrt2x+y^2+2y+2+1-3=0$
$x^2-2\sqrt2x+y^2+2y=0$
$(2\sqrt2-\sqrt2)^2+(0+1)^2=3$
$2+1=3$
---
stredova:
$l:(x-5)^2+(y+3)^2=16$
obecna:
$l:x^2-2*5*x+y^2-2y3+25+9+16=0$
$l:x^2-2*5*x+y^2-2y3+50=0$
$r=\sqrt16=4$
$S=[5;-3]$
---
$x^2-2x_sx+y^2-2y_sy+p=0$
$x^2+y^2-6x+4y+4=0$
$x^2-6x+y^2+4y+4=0$
$x^2-2*3x+y^2-2*(-2)y+4$
$+9-4-1$
$S=[9;-2]$
$r=1$
$(x-9)^2+(y+4)^2=1$
---
$x^2+y^2-6x+5y+6=0$
$x^2+y^2-2*3x+2*2.5y+6=0$
---
$x^2+y^2-4x+7=0$
$x^2+y^2-2*2x+2^2-(-3)=0$
$S=[2;0]$
$r=\sqrt{-3}=\sqrt3i$
neni
---
$x^2+y^2+4x-8y+1=0$
$x^2+y^2-2(-2)x-2*4*y+(-2)^2+4^2-19=0$
$S=[-2;4]$
$r=\sqrt{19}$
---
$2x^2+2y^2-6y-3=0$
$x^2+y^2-3y-1.5=0$
$S=[0;\frac32]$
$r=\sqrt{\frac32^2+1.5}=\sqrt{\frac64+1.5}=\sqrt{3}$

14
notes/mat/Geometrie/Analytická/Kužolosečky.md → notes/mat/Geometrie/Analytická/Kuželosečky.md
View file

@ -1,4 +1,12 @@
# Kužolosečky
# Kuželosečky
vlevo (“x”) je plocha kužele, vpravo plocha válce (“I I“)
- Někdy je nazýváme “kvadratické útvary v rovině”, protože je popisuje kvadratické rovnice.
Rozdělení:
- 1-4 regulární kuželosečky - neprochází vrcholem
- 5-9 singulární - prochází vrcholem
1. kružnice
![[Kužolosečky 2024-02-15 10.22.05.excalidraw]]
@ -25,6 +33,10 @@ protne obě “strany”
![[Kužolosečky 2024-02-15 10.44.44.excalidraw]]
7. přímka
![[Kužolosečky 2024-02-15 11.00.14.excalidraw]]
8. prázdná množina
![[Kužolosečky 2024-02-15 11.01.27.excalidraw]]
## Kuželová plocha