638 lines
18 KiB
Typst
638 lines
18 KiB
Typst
// #import "@preview/cetz:0.4.0": canvas
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// #import "@preview/cetz-plot:0.1.2": plot
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// #canvas({
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// plot.plot(
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// size: (8, 8),
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// axis-style: "school-book", // nur Achsen, kein Rahmen[web:17]
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// x-min: -2, x-max: 2, // negativer und positiver x-Bereich[web:27]
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// y-min: -1, y-max: 3.5,
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// x-tick-step: none, // automatische Ticks aus[web:24]
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// y-tick-step: none,
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// // nur 1/2 und x auf der x-Achse:
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// x-ticks: (
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// (0.5, $1/2$),
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// (1.25, $x$),
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// ),
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// // z.B. ein paar y-Ticks, falls gewünscht:
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// y-ticks: (
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// (0.25, $1/4$),
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// (1.5625, $x^2$),
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// ),
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// shared-zero: false, // optional: 0 am Ursprung ausblenden[web:16]
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// // Parabel: y = x^2 auf [-2,2]
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// plot.add(
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// domain: (-3, 3),
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// (x) => x * x,
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// )
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// )
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// })
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// #import "@preview/cetz:0.4.2"
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// #import "@preview/cetz-plot:0.1.3": plot
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// #cetz.canvas({
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// //import cetz.plot
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// //import cetz.palette
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// import cetz.draw: *
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// plot.plot(
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// size: (6, 6),
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// x-tick-step: none,
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// y-tick-step: none,
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// axis-style: "school-book",
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// x-label: $x$,
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// y-label: $y$,
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// x-ticks: (
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// (0.5, $1/2$),
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// (1.25, $x$),
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// ),
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// y-ticks: (
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// (0.25, $1/4$),
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// (1.5625, $x^2$),
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// ),
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// {
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// let f = x => calc.pow(x, 2)
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// // Definition der Punkte
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// let x0 = 0.5
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// let y0 = f(x0)
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// let x1 = 1.25
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// let y1 = f(x1)
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// // Berechnung der Steigung m = (y1 - y0) / (x1 - x0)
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// let m = (y1 - y0) / (x1 - x0)
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// // Sekantenfunktion: s(x) = m * (x - x0) + y0
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// let s = x => m * (x - x0) + y0
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// // 1. Die Parabel
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// plot.add(f, domain: (-1.3, 1.8), label: $f(x) = x^2$)
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// // 2. Die Sekante (etwas weiter gezeichnet für die Optik)
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// plot.add(s, domain: (0, 2), style: (stroke: blue))
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// // 3. Die Punkte markieren
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// plot.add(((x0, y0),), mark: "o", label: $P_0$)
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// plot.add(((x1, y1),), mark: "o", label: $P$)
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// // 4. Hilfslinien (gestrichelt)
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// plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.5pt)))
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// plot.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.5pt)))
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// plot.add(((x0, y0), (x1, y0)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
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// plot.add-anchor("pt1", (2,5))
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// }
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// )
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// // content("plot.x", [asdf])
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// })
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// #import "@preview/cetz:0.4.2"
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// #import "@preview/cetz-plot:0.1.2": plot
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// #cetz.canvas({
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// plot.plot(
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// size: (6, 6),
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// x-tick-step: 1,
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// y-tick-step: 1,
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// axis-style: "school-book",
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// x-label: $x$,
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// y-label: $y$,
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// {
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// let f = x => calc.pow(x, 2)
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// let x0 = 0.5
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// let x1 = 1.5
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// // 1. Die Parabel
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// plot.add(f, domain: (-1.3, 1.8), label: $f(x)$)
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// // 2. Die Sekante
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// let m = (f(x1) - f(x0)) / (x1 - x0)
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// plot.add(x => m * (x - x0) + f(x0), domain: (0, 2), style: (stroke: blue))
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// // 3. Hilfslinien
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// plot.add(((x0, 0), (x0, f(x0))), style: (stroke: (dash: "dashed", paint: gray)))
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// plot.add(((x1, 0), (x1, f(x1))), style: (stroke: (dash: "dashed", paint: gray)))
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// // 4. Beschriftungen OHNE den "bounds" Fehler
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// // Wir nutzen plot.add mit leeren Markern oder speziellen Labels
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// // Punkte markieren und direkt beschriften
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// plot.add(((x0, f(x0)),), mark: "o", label: $P_0$)
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// plot.add(((x1, f(x1)),), mark: "o", label: $P$)
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// // Beschriftung an der x-Achse
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// // Trick: Wir addieren einen "unsichtbaren" Punkt an der Achse mit Label
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// plot.add(((x0, 0),), label: $x_0$, mark: none)
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// plot.add(((x1, 0),), label: $x$, mark: none)
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// }
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// )
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// })
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// #import "@preview/cetz:0.4.2"
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// #import "@preview/cetz-plot:0.1.2" as cetz_plot
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// #cetz.canvas({
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// let cp = cetz_plot.plot
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// let x0 = 0.5
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// let x1 = 1.5
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// let f = x => calc.pow(x, 2)
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// let y0 = f(x0)
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// let y1 = f(x1)
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// cp.plot(
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// size: (6, 6),
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// x-tick-step: 1,
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// y-tick-step: 1,
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// axis-style: "school-book",
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// x-label: $x$,
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// y-label: $y$,
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// {
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// // 1. Die Graphen
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// cp.add(f, domain: (-1.3, 1.8))
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// let m = (y1 - y0) / (x1 - x0)
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// cp.add(x => m * (x - x0) + y0, domain: (-0.2, 2.2), style: (stroke: blue))
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// // 2. Hilfslinien
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// cp.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray)))
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// cp.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray)))
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// // 3. Punkte P0 und P
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// cp.add(((x0, y0),), mark: "o")
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// cp.add(((x1, y1),), mark: "o")
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// // 4. BESCHRIFTUNG (Der Trick: add mit mark: none)
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// // Wir setzen die Labels direkt an die Koordinaten
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// // x-Achse Beschriftung (leicht unter y=0 verschoben mit 'label-offset')
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// cp.add(((x0, 0),), label: $x_0$, mark: none)
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// cp.add(((x1, 0),), label: $x$, mark: none)
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// // Punkte beschriften
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// cp.add(((x0 - 0.1, y0 + 0.3),), label: $P_0$, mark: none)
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// cp.add(((x1 + 0.2, y1),), label: $P$, mark: none)
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// // Funktionsnamen
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// cp.add(((1.6, 3.2),), label: $f(x)$, mark: none)
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// }
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// )
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// })
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// #import "@preview/cetz:0.4.2"
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// #import "@preview/cetz-plot:0.1.2" as cetz_plot
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// #cetz.canvas({
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// import cetz.draw: *
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// let cp = cetz_plot.plot
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// // 1. Parameter festlegen
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// let (w, h) = (6, 6) // Größe des Plots
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// let x-min = -1.5
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// let x-max = 2.5
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// let y-min = -1.0
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// let y-max = 4.0
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// let x0 = 0.5
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// let x1 = 1.5
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// let f = x => calc.pow(x, 2)
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// let y0 = f(x0)
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// let y1 = f(x1)
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// // 2. Den Plot zeichnen (als Basis)
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// cp.plot(
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// size: (w, h),
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// x-tick-step: 1,
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// y-tick-step: 1,
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// axis-style: "school-book",
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// x-label: $x$,
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// y-label: $y$,
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// x-domain: (x-min, x-max),
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// y-domain: (y-min, y-max),
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// name: "p",
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// {
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// cp.add(f, domain: (x-min, x-max))
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// let m = (y1 - y0) / (x1 - x0)
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// cp.add(x => m * (x - x0) + y0, domain: (x-min, x-max), style: (stroke: blue))
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// cp.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray)))
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// cp.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray)))
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// cp.add(((x0, y0),), mark: "o")
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// cp.add(((x1, y1),), mark: "o")
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// }
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// )
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// // 3. DER FIX: Manuelle Beschriftung über das "p.origin"
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// // Wir nutzen die Größe des Plots, um die Koordinaten selbst zu setzen.
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// // Da der Ursprung im school-book Stil bei (0,0) liegt:
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// let plot-coords(x, y) = {
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// let px = (x / (x-max - x-min)) * w
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// let py = (y / (y-max - y-min)) * h
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// return (rel: (px, py), to: "p.origin")
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// }
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// // Beschriftungen (Diese liegen nun außerhalb des Plot-Berechnungs-Logik)
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// content(plot-coords(x0, -0.4), $x_0$)
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// content(plot-coords(x1, -0.4), $x$)
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// content(plot-coords(x0 - 0.3, y0 + 0.3), $P_0$)
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// content(plot-coords(x1 + 0.3, y1), $P$)
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// content(plot-coords(1.6, 3.2), $f(x)$)
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// })
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// #import "@preview/cetz:0.4.2"
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// #cetz.canvas({
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// import cetz.draw: *
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// // 1. Koordinatensystem manuell skalieren (1 Einheit = 1.5cm)
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// scale(1.5)
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// // Parameter
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// let x0 = 0.5
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// let x1 = 1.5
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// let f(x) = calc.pow(x, 2)
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// let y0 = f(x0)
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// let y1 = f(x1)
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// // 2. Achsen zeichnen (School-Book)
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// line((-1.5, 0), (2.5, 0), mark: (end: ">"), name: "xaxis")
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// line((0, -1), (0, 4), mark: (end: ">"), name: "yaxis")
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// content((2.5, -0.3), $x$)
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// content((-0.3, 4), $y$)
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// // 3. Parabel zeichnen (Sampling-Methode: Sicherster Weg ohne Extra-Module)
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// let points = ()
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// for i in range(-13, 19) {
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// let x = i / 10
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// points.push((x, f(x)))
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// }
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// line(..points, stroke: black)
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// // 4. Sekante zeichnen
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// let m = (y1 - y0) / (x1 - x0)
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// // Gerade: y = m*(x - x0) + y0
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// line((-0.5, m * (-0.5 - x0) + y0), (2.2, m * (2.2 - x0) + y0), stroke: blue)
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// // 5. Hilfslinien & Punkte
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// line((x0, 0), (x0, y0), stroke: (dash: "dashed", paint: gray))
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// line((x1, 0), (x1, y1), stroke: (dash: "dashed", paint: gray))
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// circle((x0, y0), radius: 0.05, fill: black)
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// circle((x1, y1), radius: 0.05, fill: black)
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// // 6. BESCHRIFTUNGEN (Direkt an den Objekten)
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// content((x0, -0.4), $x_0$)
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// content((x1, -0.4), $x$)
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// content((x0 - 0.3, y0 + 0.2), $P_0$)
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// content((x1 + 0.3, y1), $P$)
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// content((1.8, f(1.8)), $f(x)$, anchor: "west", padding: .1)
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// content((2.1, 3.5), [Sekante], fill: white, padding: .1)
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// })
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// #import "@preview/cetz:0.4.2"
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// #cetz.canvas({
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// import cetz.draw: *
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// // 1. Koordinatensystem manuell skalieren (1 Einheit = 1.5cm)
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// scale(1.5)
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// // Parameter
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// let x0 = 0.5
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// let x1 = 1.5
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// let f(x) = calc.pow(x, 2)
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// let y0 = f(x0)
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// let y1 = f(x1)
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// // 2. Achsen zeichnen (School-Book)
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// line((-1.5, 0), (2.5, 0), mark: (end: ">"), name: "xaxis")
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// line((0, -1), (0, 4), mark: (end: ">"), name: "yaxis")
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// content((2.5, -0.3), $x$)
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// content((-0.3, 4), $y$)
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// // 3. Parabel zeichnen (Sampling-Methode: Sicherster Weg ohne Extra-Module)
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// let points = ()
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// for i in range(-13, 19) {
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// let x = i / 10
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// points.push((x, f(x)))
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// }
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// line(..points, stroke: black)
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// // 4. Sekante zeichnen
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// let m = (y1 - y0) / (x1 - x0)
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// // Gerade: y = m*(x - x0) + y0
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// line((-0.5, m * (-0.5 - x0) + y0), (2.2, m * (2.2 - x0) + y0), stroke: blue)
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// // 5. Hilfslinien & Punkte
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// line((x0, 0), (x0, y0), stroke: (dash: "dashed", paint: gray))
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// line((x1, 0), (x1, y1), stroke: (dash: "dashed", paint: gray))
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// circle((x0, y0), radius: 0.05, fill: black)
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// circle((x1, y1), radius: 0.05, fill: black)
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// // 6. BESCHRIFTUNGEN (Direkt an den Objekten)
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// content((x0, -0.4), $x_0$)
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// content((x1, -0.4), $x$)
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// content((x0 - 0.3, y0 + 0.2), $P_0$)
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// content((x1 + 0.3, y1), $P$)
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// content((1.8, f(1.8)), $f(x)$, anchor: "west", padding: .1)
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// content((2.1, 3.5), [Sekante], fill: white, padding: .1)
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// })
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// #import "@preview/cetz:0.4.2"
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// #align(center,
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// cetz.canvas({
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// // import cetz.plot
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// import cetz.palette
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// import cetz.draw: *
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// plot.plot(size: (5,5),
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// name: "plot",
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// x-tick-step: 2,
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// x-minor-tick-step: 1,
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// y-tick-step: 6,
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// y-minor-tick-step: 1,
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// axis-style: "school-book", {
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// plot.add(domain: (-2.5, 2.5),
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// x => (4-calc.pow(x, 2)),
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// style: palette.tango-light)
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// plot.add(domain: (-2.5, 2.5),
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// x => (4-2*x),
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// style: palette.tango-light)
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// plot.add-fill-between(domain: (0, 2),
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// x => (4-calc.pow(x, 2)),
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// x => (4-2*x),
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// style: palette.tango-light)
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// plot.add(((0,4), (2,0)),
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// mark: "o",
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// mark-style: (stroke: none, fill: black),
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// style: (stroke: none))
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// plot.add-anchor("pt1", (2,5))
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// plot.add-anchor("pt2", (-2,5.5))
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// plot.add-anchor("parab", (1, 4-calc.pow(1, 2)+0.2))
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// plot.add-anchor("rline", (-1.5, 4-2*(-1.5)-0.2))
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// })
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// content("plot.pt1", [$y=4-2x^2$], anchor: "south", name: "prb")
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// line("plot.parab", "prb", mark: (start: ">"))
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// content("plot.pt2", [$y=4-2x$], anchor: "north", name: "curve2")
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// line("plot.rline", "curve2", mark: (start: ">"))
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// })
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// )
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// #align(center,
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// cetz.canvas({
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// // import cetz.plot
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// // import cetz.palette
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// import cetz.draw: *
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// plot.plot(
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// size: (6,6),
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// name: "plot",
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// x-tick-step: none,
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// y-tick-step: none,
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// x-label: $x$,
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// y-label: $y$,
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// x-ticks: ((0.5, $1/2$),(1.25, $x$),),
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// y-ticks: ((0.25, $1/4$),(1.5625, $x^2$),),
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// axis-style: "school-book",
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// plot.add(
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// domain: (-1.3, 1.8),
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// x => (calc.pow(x, 2)),
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// )
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// )}))
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// #import "@preview/cetz:0.4.2"
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// #import "@preview/cetz-plot:0.1.3": plot
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// #cetz.canvas({
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// //import cetz.plot
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// //import cetz.palette
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// import cetz.draw: *
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// plot.plot(
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// size: (6, 6),
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// x-tick-step: none,
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// y-tick-step: none,
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// axis-style: "school-book",
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// x-label: $x$,
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// y-label: $y$,
|
|
// x-ticks: (
|
|
// (0.5, $1/2$),
|
|
// (1.25, $x$),
|
|
// ),
|
|
// y-ticks: (
|
|
// (0.25, $1/4$),
|
|
// (1.5625, $x^2$),
|
|
// ),
|
|
// {
|
|
// let f = x => calc.pow(x, 2)
|
|
|
|
// // Definition der Punkte
|
|
// let x0 = 0.5
|
|
// let y0 = f(x0)
|
|
// let x1 = 1.25
|
|
// let y1 = f(x1)
|
|
|
|
// // Berechnung der Steigung m = (y1 - y0) / (x1 - x0)
|
|
// let m = (y1 - y0) / (x1 - x0)
|
|
// // Sekantenfunktion: s(x) = m * (x - x0) + y0
|
|
// let s = x => m * (x - x0) + y0
|
|
|
|
// // 1. Die Parabel
|
|
// plot.add(f, domain: (-1.3, 1.8), label: $f(x) = x^2$)
|
|
|
|
// // 2. Die Sekante (etwas weiter gezeichnet für die Optik)
|
|
// plot.add(s, domain: (0, 2), style: (stroke: blue))
|
|
|
|
// // 3. Die Punkte markieren
|
|
// plot.add(((x0, y0),), mark: "o", label: $P_0$)
|
|
// plot.add(((x1, y1),), mark: "o", label: $P$)
|
|
|
|
// // 4. Hilfslinien (gestrichelt)
|
|
// plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.5pt)))
|
|
// plot.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.5pt)))
|
|
|
|
// plot.add(((x0, y0), (x1, y0)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
|
|
|
|
|
|
// plot.add-anchor("pt1", (2,5))
|
|
// }
|
|
|
|
// )
|
|
// // content("plot.x", [asdf])
|
|
// })
|
|
|
|
|
|
#import "@preview/cetz:0.4.2"
|
|
#import "@preview/cetz-plot:0.1.3": plot
|
|
|
|
#cetz.canvas({
|
|
import cetz.draw: *
|
|
plot.plot(
|
|
//definitionen
|
|
{
|
|
//berechnungen und plot
|
|
}
|
|
)
|
|
})
|
|
|
|
#import "@preview/cetz:0.4.2"
|
|
#import "@preview/cetz-plot:0.1.3": plot
|
|
|
|
#cetz.canvas(length: 1.25cm,{
|
|
import cetz.draw: *
|
|
set-style(
|
|
axes: (
|
|
// Basisstil beibehalten
|
|
stroke: (thickness: 0.5pt),
|
|
// x-Achse: stealth-Pfeil am Ende
|
|
x: (mark: (end: "stealth", fill: black)),
|
|
// y-Achse: stealth-Pfeil am Ende
|
|
y: (mark: (end: "stealth", fill: black)),
|
|
),
|
|
)
|
|
plot.plot(
|
|
//definitionen
|
|
name: "plot",
|
|
size: (6, 6),
|
|
x-tick-step: none,
|
|
y-tick-step: none,
|
|
axis-style: "school-book",
|
|
x-label: $x$,
|
|
y-label: $y$,
|
|
x-ticks: ((0.5, $1/2$),(1.25, $x$),),
|
|
y-ticks: ((0.25, $1/4$),(1.5625, $x^2$),),
|
|
{
|
|
//berechnungen und plot
|
|
let f = x => calc.pow(x, 2)
|
|
let x0 = 0.5
|
|
let y0 = f(x0)
|
|
let x1 = 1.25
|
|
let y1 = f(x1)
|
|
// Berechnung der Steigung m = (y1 - y0) / (x1 - x0)
|
|
let m = (y1 - y0) / (x1 - x0)
|
|
|
|
|
|
// Sekantenfunktion: s(x) = m * (x - x0) + y0
|
|
let s = x => m * (x - x0) + y0
|
|
|
|
let x1_1 = x1 + 0.1
|
|
let x0_1 = x0 - 0.2
|
|
let y0_1 = y0 + 0.2
|
|
let x2 = ((x1 - x0)/2) + x0
|
|
let y3 = ((y1 - y0)/2) +y0
|
|
|
|
plot.add(x => calc.pow(x, 2), domain: (-1.4, 1.8))
|
|
//Sekante
|
|
plot.add(s, domain: (0.3, 1.7), style: (stroke: red))
|
|
plot.add-anchor("pt1", (-1.4,y1))
|
|
plot.add-anchor("P", (x1_1,y1))
|
|
plot.add-anchor("P0", (x0_1,y0_1))
|
|
|
|
plot.add-anchor("F1", (x2,0.14))
|
|
plot.add-anchor("F2", (x1+0.1,y3))
|
|
|
|
|
|
plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
plot.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
plot.add(((0, y1), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
plot.add(((0, y0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
|
|
plot.add(((x0, y0), (x1, y0)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
|
|
plot.add(((x1, y0), (x1, y1)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
|
|
|
|
|
|
plot.add(((x0, y0),), mark: "o")
|
|
plot.add(((x1, y1),), mark: "o")
|
|
|
|
|
|
|
|
}
|
|
)
|
|
//Der Plot muss einen Namen haben
|
|
content("plot.pt1", text(0.85em)[$y=x^2$], anchor: "east", name: "pt")
|
|
content("plot.P", text(0.75em)[$P$], anchor: "west", name: "p")
|
|
content("plot.P0", text(0.75em)[$P_0$], anchor: "west", name: "p0")
|
|
content("plot.F1", text(0.75em)[$x- 1/2$], anchor: "center", name: "f1")
|
|
content("plot.F2", text(0.75em)[$x^2- 1/4$], anchor: "west", name: "f2")
|
|
})
|
|
|
|
#import "@preview/cetz:0.4.2"
|
|
#import "@preview/cetz-plot:0.1.3": plot
|
|
|
|
#cetz.canvas({
|
|
|
|
import cetz.draw: *
|
|
set-style(
|
|
axes: (
|
|
// Basisstil beibehalten
|
|
stroke: (thickness: 0.5pt),
|
|
// x-Achse: stealth-Pfeil am Ende
|
|
x: (mark: (end: "stealth", fill: black)),
|
|
// y-Achse: stealth-Pfeil am Ende
|
|
y: (mark: (end: "stealth", fill: black)),
|
|
),
|
|
)
|
|
plot.plot(
|
|
name: "plot",
|
|
size: (5, 5),
|
|
x-tick-step: none,
|
|
y-tick-step: none,
|
|
axis-style: "school-book",
|
|
x-label: $x$,
|
|
y-label: $y$,
|
|
x-ticks: ((0.5, $1/2$),),
|
|
y-ticks: ((1, $1$),),
|
|
|
|
//definitionen
|
|
{
|
|
let f = x => if x != 0.5 { (calc.pow(x, 2) - 0.25) / (x - 0.5) } else { none }
|
|
let x0 = 0.5
|
|
let y0 = 1
|
|
plot.add(f, domain: (-0.6, 0.75), style: (stroke: blue))
|
|
|
|
plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
|
|
plot.add(((0, y0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
|
|
|
|
plot.add(((x0, y0),), mark: "o")
|
|
|
|
plot.add-anchor("F1", (-.7,0.5))
|
|
plot.add-anchor("F2", (-.7,0.35))
|
|
}
|
|
)
|
|
content("plot.F1", text(0.85em)[$y=(x^2-1/4)/(x-1/2)$], anchor: "west", name: "pt")
|
|
content("plot.F2", text(0.85em)[$(x eq.not 1/2)$], anchor: "west", name: "pt")
|
|
})
|
|
|