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Daniel Bulant 2023-09-20 11:40:07 +02:00
parent 90c490b70e
commit 5547e47ce7
11 changed files with 417 additions and 390 deletions
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12
notes/.obsidian/plugins/obsidian-activity-history/data.json vendored
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2
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77
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639
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1
notes/kbb/kbb.md
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@ -8,5 +8,6 @@ imagePrefix: 'data/'
```
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[kbb/haxagon/haxagon|haxagon]]
- [[kbb/math/math|math]]
- [[kbb/tools/tools|tools]]
%% Zoottelkeeper: End of the autogenerated index file list %%

35
notes/kbb/math/Modulární aritmetika.md Normal file
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@ -0,0 +1,35 @@
# Modulární aritmetika
## Grupy
### Omezenost
### Existence neutrálního prvku
$$(\forall x \in M)(\exists n \in M)(x \cdot n=n \cdot x=x)$$
### Existence inverzního prvky
$$(\forall x\in M)(\exists i \in M)(x\cdot i=n)$$
---
## Příklady
$a+_6b=mod(a+b,6)$
$$3+_69+_610=3+3+4=4$$
$$35+_{14}33+_{14}17=35+_{14}33+_{14}17=85+_{14}=1$$
$$34+_{16}+38_{16}+_{16}42=2+6_{16}+_{16}10=2$$
---
## Inverze
Pro zjištění inverzního čísla lze použít Rozšířený Euklidův algoritmus
$5\in\mathbb{Z}_{131}$
| | $\alpha$ | $\beta$ | q |
| ------- | -------- | ------- | --- |
| $a=131$ | 1 | 0 | |
| $b=131$ | 0 | 1 | 26 |
| 1 | 1 | -26 | |
$5^{-1}105$

3
notes/kbb/math/math.md Normal file
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@ -0,0 +1,3 @@
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[kbb/math/Modulární aritmetika|Modulární aritmetika]]
%% Zoottelkeeper: End of the autogenerated index file list %%

4
notes/mat/Geometrie/Geometrie.md Normal file
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@ -0,0 +1,4 @@
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[mat/Geometrie/Konstrukční úlohy|Konstrukční úlohy]]
- [[mat/Geometrie/Zobrazení v rovině|Zobrazení v rovině]]
%% Zoottelkeeper: End of the autogenerated index file list %%

0
notes/mat/Konstrukční úlohy.md → notes/mat/Geometrie/Konstrukční úlohy.md
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32
notes/mat/Geometrie/Zobrazení v rovině.md Normal file
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@ -0,0 +1,32 @@
# Zobrazení v rovině
## Zobrazení Z v rovině
Předpis, který každému bodu $X$ z roviny přiřadí právě 1 bod $X'$ roviny
Píšeme: $Z:|\rightarrow X'$
## Samodružný bod zobrazení
Bod, pro který platí $X=X'$
bod který se zobrazí sám do sebe
## Nebodová samodružnost
Příklad: Kružnice je samodružná jestliže její střed leží na ose při osové souměrnosti, avšak její body nikoliv.
## Shodné zobrazení
Zobrazení, kde platí shodnost mezi původním objektem a cílovým.
> [!NOTE]
>
Zobrazení (v rovině) je **shodné zobrazení**, právě když obrazem každé úsečky $AB$ je úsečka $A'B'$ shodná s úsečkou $AB$.
Zachovává vzdálenost a velikosti úseček, tím pádem také:
- velikosti úhlů
- rovnoběžnost
- typ objektu (přímka na přímku, kružnice na kružnici apod.)
Příklady:
- osová souměrnost
- středová souměrnost
- posunutí
- otočení

2
notes/mat/mat.md
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@ -13,8 +13,8 @@ imagePrefix: 'data/'
- [[mat/Druhá odmocnina|Druhá odmocnina]]
- [[mat/Ekvigonala|Ekvigonala]]
- [[mat/Funkce/Funkce|Funkce]]
- [[mat/Geometrie/Geometrie|Geometrie]]
- [[mat/Intervaly|Intervaly]]
- [[mat/Konstrukční úlohy|Konstrukční úlohy]]
- [[mat/Lomené výrazy/Lomené výrazy|Lomené výrazy]]
- [[mat/Lomené výrazy|Lomené výrazy]]
- [[mat/Matematika|Matematika]]