From c01e04918d09d6c4f76d715435defedd5048612c Mon Sep 17 00:00:00 2001
From: Sven Riwoldt <sven.riwoldt@web.de>
Date: Fri, 20 Feb 2026 19:41:25 +0100
Subject: [PATCH] Beginn typst

---
 FHTW.typ                   |  73 ++++++++++++++++++
 LineareAlgebraGrafiken.typ | 152 +++++++++++++++++++++++++++++++++++++
 2 files changed, 225 insertions(+)
 create mode 100644 FHTW.typ
 create mode 100644 LineareAlgebraGrafiken.typ

diff --git a/FHTW.typ b/FHTW.typ
new file mode 100644
index 0000000..d4f8dd4
--- /dev/null
+++ b/FHTW.typ
@@ -0,0 +1,73 @@
+#import "@preview/cetz:0.4.2"
+#import "LineareAlgebraGrafiken.typ": * 
+
+#set page(
+  margin: 2cm,
+  paper: "a4"
+  )
+
+#title("Mathematik FHTW Berlin")
+
+= Lineare Algebra
+== Vektoren
+=== Veranschaulichung von Vektoren in der Ebene
+
+#show math.equation: set text(font: "New Computer Modern Sans Math", size: 12pt)
+
+#show math.equation.where(block: false): it => math.display(it)
+
+
+//#set page(width: auto, height: auto, margin: .5cm)
+
+#table(
+  columns: 3,
+  stroke: none,
+  [#abb1()],[#h(1cm)], [#abb2()]
+)//&#show math.equation: block.with(fill: white, inset: 1pt)
+
+
+
+
+
+$arrow(a)=(a_1, a_2)$, auch üblich $arrow(a)=vec(a_1, a_2) arrow.l$ geordnetes Paar
+
+=== Menge aller Vektoren in der Ebene
+Die Menge aller Vektoren in der Ebene heißt $RR^2$; dabei ist $RR$ die Menge der reellen Zahlen. 
+
+Also: $RR={arrow(a)=(a_1,a_2) | a_1 in RR, a_2 in RR }$
+
+
+=== Addition von Vektoren in der Ebene
+- liefert wieder einen Vektor
+- rechnerisch: 
+  - $arrow(a)=(a_1, a_2)$, $arrow(b)=(b_1, b_2)$ 
+  - $arrow(a)+arrow(b)=(a_1+b_1, a_2+b_2)$  
+
+#abb3()
+
+
+/*1.1.2 Menge aller Vektoren in der Ebene
+
+Die Menge aller Vektoren in der Ebene heißt $\mathbb{R}^2$; dabei ist $\mathbb{R}$ die Menge der reellen Zahlen. Also: $\mathbb{R}=\left\{\vec{a}=\left(a_1, a_2\right) \mid a_1 \in \mathbb{R}, a_2 \in \mathbb{R}\right\}$
+1.1.3 Addition von Vektoren in der Ebene
+
+Die Addition von Vektoren liefert als Ergebnis wieder einen Vektor.
+rechnerisch:
+
+$$
+\begin{aligned}
+& \vec{a}=\left(a_1, a_2\right), \vec{b}=\left(b_1, b_2\right) \\
+& \vec{a}+\vec{b}=\left(\left(a_1+b_1, a_2+b_2\right)\right)
+\end{aligned}
+$$
+
+zeichnerisch:
+
+Rechenregeln:
+
+$$
+\begin{aligned}
+& \vec{a}+\vec{b}=\vec{b}+\vec{a} \\
+& \vec{a}+(\vec{b}+\vec{c})=(\vec{a}+\vec{b})+\vec{c}
+\end{aligned}
+$$*/
\ No newline at end of file
diff --git a/LineareAlgebraGrafiken.typ b/LineareAlgebraGrafiken.typ
new file mode 100644
index 0000000..ad26a9a
--- /dev/null
+++ b/LineareAlgebraGrafiken.typ
@@ -0,0 +1,152 @@
+#import "@preview/cetz:0.3.3" //Grafiken
+
+#let abb1() = {
+
+cetz.canvas(length: 3cm, {
+  import cetz.draw: *
+
+  set-style(
+    mark: (fill: black, scale: 2),
+    stroke: (thickness: 0.4pt, cap: "round"),
+    angle: (
+      radius: 0.3,
+      label-radius: .22,
+      fill: green.lighten(80%),
+      stroke: (paint: green.darken(50%))
+    ),
+    content: (padding: 1pt)
+  )
+
+  grid((-.25, -.25), (2, 2 ), step: 0.5, stroke: gray + 0.2pt)
+
+
+
+  line((-.25, 0), (1.85, 0), mark: (end: "stealth"))
+  content((), $ x $, anchor: "west")
+  line((0, -.25), (0, 1.85), mark: (end: "stealth"))
+  content((), $ y $, anchor: "south")
+
+  for (x, ct) in ((0, $ 0 $), (0.5, $ 1 $), (1, $ 2 $), (1.5, $ 3 $), (1.25, $a_1$)) {
+    line((x, 3pt), (x, -3pt))
+    content((), anchor: "north", ct)
+  }
+
+  for (y, ct) in ((0.5, $ 1 $), (1, $ 2 $), (1.5, $ 3 $), (1.25, $a_2$)) {
+    line((3pt, y), (-3pt, y))
+    content((), anchor: "east", ct)
+  }
+
+  
+
+  //line((0,0), (1.25, 1.25),name: "vec",mark: (end: "stealth", fill: green.darken(30%)),
+  //stroke: (paint: green.darken(30%), thickness: 1.25pt))
+
+line((0,0), (1.25, 1.25),name: "vec",stroke: (paint: red.darken(30%), thickness: 1.25pt))
+
+
+  line((1.25,0), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.75pt))
+
+  line((0,1.25), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.75pt))
+
+circle((1.25,1.25), radius: 0.025, fill: green.darken(30%), stroke: (paint: green.darken(30%), thickness: 1.25pt), name: "punkt")
+  content("punkt.end", anchor: "south-west", padding: (left: 3mm, bottom: 2mm),  text(green.darken(30%))[Punkt $(a_1, a_2)$])})
+}
+
+#let abb2() = {
+  cetz.canvas(length: 3cm, {
+  import cetz.draw: *
+
+  set-style(
+    mark: (fill: black, scale: 2),
+    stroke: (thickness: 0.4pt, cap: "round"),
+    angle: (
+      radius: 0.3,
+      label-radius: .22,
+      fill: green.lighten(80%),
+      stroke: (paint: green.darken(50%))
+    ),
+    content: (padding: 1pt)
+  )
+
+  grid((-.25, -.25), (2, 2 ), step: 0.5, stroke: gray + 0.2pt)
+
+
+
+  line((-.25, 0), (1.85, 0), mark: (end: "stealth"))
+  content((), $ x $, anchor: "west")
+  line((0, -.25), (0, 1.85), mark: (end: "stealth"))
+  content((), $ y $, anchor: "south")
+
+  for (x, ct) in ((0, $ 0 $), (0.5, $ 1 $), (1, $ 2 $), (1.5, $ 3 $), (1.25, $a_1$)) {
+    line((x, 3pt), (x, -3pt))
+    content((), anchor: "north", ct)
+  }
+
+  for (y, ct) in ((0.5, $ 1 $), (1, $ 2 $), (1.5, $ 3 $), (1.25, $a_2$)) {
+    line((3pt, y), (-3pt, y))
+    content((), anchor: "east", ct)
+  }
+
+
+line((0,0), (1.25, 1.25),name: "vec",stroke: (paint: red.darken(30%), thickness: 1.25pt))
+
+
+  line((1.25,0), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.75pt))
+
+  line((0,1.25), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.75pt))
+
+  line((0,0), (1.25, 1.25),name: "vec",mark: (end: "stealth", fill: green.darken(30%)), stroke: (paint: green.darken(30%), thickness: 1.25pt))
+
+  content("vec.end", anchor: "north-west", padding: (left: 3mm, top: -2mm), text(green.darken(30%))[Vektor $arrow(a)$])
+})
+
+}
+
+#let abb3() = {
+  cetz.canvas(length: 37mm,
+   {
+  import cetz.draw: *
+
+  set-style(
+    mark: (fill: black, scale: 2),
+    stroke: (thickness: 0.4pt, cap: "round"),
+    angle: (
+      radius: 0.3,
+      label-radius: .22,
+      fill: green.lighten(80%),
+      stroke: (paint: green.darken(50%))
+    ),
+    content: (padding: 1pt)
+  )
+
+  grid((-.25, -.25), (2.5 , 2 ), step: 0.5, stroke: gray + 0.2pt)
+
+    line((-.25, 0), (2.25, 0), mark: (end: "stealth"))
+  content((), $ x $, anchor: "west")
+  line((0, -.25), (0, 1.85), mark: (end: "stealth"))
+  content((), $ y $, anchor: "south")
+
+  for (x, ct) in ((0.25, $ 1 $), (0.5, $ 2$), (0.75, $ a_1 $),(1, $b_1$), (1.25,$5$), (1.5, $6$),(1.75, $a_1+b_1$)) {
+    line((x, 3pt), (x, -3pt))
+    content((), anchor: "north", ct)
+  }
+
+  for (y, ct) in ((0.25, $ 1 $), (0.5, $ a_2 $), (.75, $ 3 $), (1., $b_2$),(1.25,$5$), (1.5, $6$)) {
+    line((3pt, y), (-3pt, y))
+    content((), anchor: "east", ct)
+  }
+
+  line((0,0), (0.75, .5),name: "veca",mark: (end: "stealth", fill: blue.darken(30%)), stroke: (paint: blue.darken(30%), thickness: 0.75pt))
+  
+  content("veca.100%", anchor: "west", padding: (left:1mm, bottom:-5mm),text(blue.darken(30%))[$arrow(a)$])
+
+  line((0,0), (1, 1),name: "vecb",mark: (end: "stealth", fill: red.darken(30%)), stroke: (paint: red.darken(30%), thickness: 0.75pt))
+
+  content("vecb.80%", anchor: "east", padding: (left:0mm, bottom:5mm),text(red.darken(30%))[$arrow(b)$])
+
+  //
+
+  //line((0,0), (1.5, 1),name: "vecb",mark: (end: "stealth", fill: red), stroke: (paint: red, thickness: 0.75pt))
+
+
+  })}
\ No newline at end of file