vault backup: 2023-09-20 11:40:07

notes/.obsidian/plugins/obsidian-activity-history/data.json

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notes/.obsidian/plugins/various-complements/histories.json

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notes/kbb/kbb.md

@@ -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  %%

notes/kbb/math/Modulární aritmetika.md

@@ -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     |     |
+
+$5^{-1}105$

notes/kbb/math/math.md

@@ -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  %%

notes/mat/Geometrie/Geometrie.md

@@ -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  %%

notes/mat/Geometrie/Zobrazení v rovině.md

@@ -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
+

notes/mat/mat.md

@@ -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]]