FHTW Typst bei Abbildung 4

FHTW.typ

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+#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
+#table(
+  columns: 2,
+  stroke: none,
+  [- liefert wieder einen Vektor
+- rechnerisch: 
+  - $arrow(a)=(a_1, a_2)$, $arrow(b)=(b_1, b_2)$ 
+  - $arrow(a)+arrow(b)=(a_1+b_1, a_2+b_2)$ 
+- Rechenregeln:
+  - $arrow(a)+arrow(b)=arrow(b)+arrow(a)$
+  - $arrow(a)+(arrow(b)+arrow(c)))$; $(arrow(a)+arrow(b))=arrow(c)$],[zeichnerisch:#abb3()]
+)
+
+#pagebreak()
+=== Nullvektor in der Ebene
+
+- $arrow(0)=(0,0)$
+- Rechenregel: $arrow(a)+arrow(0)=arrow(a)$
+
+=== Subtraktion von Vektoren in der Ebene
+
+#table(
+  columns: 2,
+  stroke: none,
+  [- liefert wieder einen Vektor
+- rechnerisch:
+  - $arrow(a)=(a_1,a_2)$, $arrow(b)=(b_1, b_2)$
+  - $arrow(a)-arrow(b)= (a_1-b_1, a_2-b_2$)  ],[#abb4()]
+)
+

LineareAlgebraGrafiken.typ

@@ -0,0 +1,205 @@
+#import "@preview/cetz:0.3.3" //Grafiken
+#set text(font: "New Computer Modern Sans Math")
+
+#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((-.05, 0), (1.85, 0), mark: (end: "stealth", scale: 0.8))
+  content((), $ x $, anchor: "west")
+  line((0, -.05), (0, 1.85), mark: (end: "stealth", scale: 0.8))
+  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: 0.5pt))
+
+  line((0,1.25), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.5pt))
+
+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((-.05, 0), (1.85, 0), mark: (end: "stealth", scale: 0.8))
+  content((), $ x $, anchor: "west")
+  line((0, -.05), (0, 1.85), mark: (end: "stealth", scale: 0.8))
+  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: 0.5pt))
+
+  line((0,1.25), (1.25, 1.25), stroke: (dash: "dashed", paint: blue.darken(30%), thickness: 0.5pt))
+
+  line((0,0), (1.25, 1.25),name: "vec",mark: (end: "stealth", fill: green.darken(30%),scale: 0.8), 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: 40mm,
+   {
+  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((-.05, 0), (80mm, 0), mark: (end: "stealth",scale: 0.9))
+  content((), $ x $, anchor: "west")
+  line((0, -.05), (0, 70mm), mark: (end: "stealth",scale: 0.9))
+  content((), $ y $, anchor: "south")
+
+  for (x, ct) in ((10mm, $ 1 $), (20mm, $ b_1$), (30mm, $ 3 $),(40mm, $a_1$), (50mm,$5$), (60mm, $a_1 + b_1$),(70mm, $7$)) {
+    line((x, 3pt), (x, -3pt))
+    content((), anchor: "north", ct)
+  }
+
+  for (y, ct) in ((10mm, $ a_2 $), (20mm, $ 2 $), (30mm, $ 3 $), (40mm, $b_2$),(1.25,$a_2+b_2$), (1.5, $6$)) {
+    line((3pt, y), (-3pt, y))
+    content((), anchor: "east", ct)
+  }
+
+  line((0,0), (40mm, 10mm),name: "veca",mark: (end: "stealth", fill: blue.darken(30%),scale:0.9), 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((40mm,0), (40mm, 10mm ), stroke: (dash: "dotted",paint: blue.darken(30%), thickness: 0.5pt))
+
+ line((0,10mm), (40mm, 10mm), stroke: (dash: "dotted",paint: blue.darken(30%), thickness: 0.5pt))
+ 
+ line((0,0), (20mm, 40mm),name: "vecb",mark: (end: "stealth", fill: red.darken(30%),scale: 0.9), 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((20mm,0mm), (20mm, 40mm), stroke: (dash: "dotted",paint: red.darken(30%), thickness: 0.5pt))
+
+ line((0mm,40mm), (20mm, 40mm), stroke: (dash: "dotted",paint: red.darken(30%), thickness: 0.5pt))
+
+ line((0,0), (60mm, 50mm),name: "vec_ab",mark: (end: "stealth", fill: orange ,scale: 0.9), stroke: (paint: orange, thickness: 0.75pt))
+
+ content("vec_ab.100%", anchor: "east", padding: (left:0mm, bottom:5mm),text(green.darken(60%))[$arrow(a) + arrow(b)$])
+
+ line((20mm,40mm), (60mm, 50mm),name: "veca_dotted",mark: (end: "stealth", scale: 0.9), stroke: (dash: "dotted", paint: blue, thickness: 0.75pt))
+ 
+ line((40mm,10mm), (60mm, 50mm),name: "vecb_dotted",mark: (end: "stealth", scale: 0.9), stroke: (dash: "dotted", paint: red, thickness: 0.75pt))
+
+ content((50mm, 20mm), [Parallelogramm])
+
+  arc(
+    (48mm, 18mm),
+    radius: 0.25,
+    start: -45deg,
+    delta: -90deg,
+    mark: (
+      end: "stealth",
+    ))
+
+  line((60mm,0mm), (60mm, 50mm),name: "vecab_dotted", stroke: (dash: "dotted", paint: orange, thickness: 0.75pt))
+
+  line((0mm,50mm), (60mm, 50mm),name: "vecab_dotted",stroke: (dash: "dotted", paint: orange, thickness: 0.75pt))
+    
+  })}
+
+  #let abb4() = {
+
+      cetz.canvas(length: 40mm,
+   {
+  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((-30mm, 0), (50mm, 0), mark: (end: "stealth",scale: 0.9))
+  content((), $ x $, anchor: "west")
+  line((0, -.05), (0, 70mm), mark: (end: "stealth",scale: 0.9))
+  content((), $ y $, anchor: "south")
+
+  
+})
+    
+  }