Chapter 3.3-3.6: Manim Complete Guide

Math Functions, 3D Graphics, and Final Projects

🎨 PROJECTS 3.3-3.6 | Difficulty: Intermediate-Advanced

Note

Special Note: This project is designed for students who have completed the first chapter of CS Quests and are familiar with Python basics. If you’re new to programming, consider starting with the earlier lessons before diving into this project.

Another Special Note: This project requires a local Python environment for full functionality. While we provide examples and code snippets here, some features may not run directly in the browser. For the best experience, consider setting up the project on your own computer.

3.3: Mathematical Functions & Graphs

Plotting Functions

from manim import *

class PlotFunction(Scene):
    def construct(self):
        # Create axes
        axes = Axes(
            x_range=[-5, 5, 1],
            y_range=[-3, 3, 1],
            axis_config={"color": BLUE}
        )
        
        # Plot functions
        parabola = axes.plot(lambda x: x**2 / 4, color=RED)
        sine = axes.plot(lambda x: np.sin(x), color=GREEN)
        
        # Labels
        labels = axes.get_axis_labels(x_label="x", y_label="f(x)")
        
        # Animate
        self.play(Create(axes), Write(labels))
        self.play(Create(parabola))
        self.wait(1)
        self.play(Transform(parabola, sine))
        self.wait(1)

LaTeX Equations

class LatexDemo(Scene):
    def construct(self):
        # Beautiful mathematical notation
        equation = MathTex(r"f(x) = \frac{1}{2}x^2 + 3x - 5")
        equation.scale(1.5)
        
        self.play(Write(equation))
        self.wait(1)
        
        # Transform to derivative
        derivative = MathTex(r"f'(x) = x + 3")
        derivative.scale(1.5)
        
        self.play(TransformMatchingTex(equation, derivative))
        self.wait(1)

3.4: Calculus Visualizations

Derivative Visualization

class DerivativeDemo(Scene):
    def construct(self):
        axes = Axes(x_range=[-3, 3], y_range=[-1, 9])
        curve = axes.plot(lambda x: x**2, color=BLUE)
        
        # Moving tangent line
        def get_tangent_line(x):
            slope = 2 * x  # derivative of x^2
            point = axes.c2p(x, x**2)
            line = Line(
                point + LEFT * 1.5 + DOWN * slope * 1.5,
                point + RIGHT * 1.5 + UP * slope * 1.5,
                color=RED
            )
            return line
        
        tangent = always_redraw(lambda: get_tangent_line(x_tracker.get_value()))
        x_tracker = ValueTracker(-2)
        
        self.add(axes, curve, tangent)
        self.play(x_tracker.animate.set_value(2), run_time=4)

Area Under Curve (Integration)

class IntegralDemo(Scene):
    def construct(self):
        axes = Axes(x_range=[0, 4], y_range=[0, 20])
        curve = axes.plot(lambda x: x**2, color=BLUE)
        
        # Riemann rectangles
        rectangles = axes.get_riemann_rectangles(
            curve,
            x_range=[0, 3],
            dx=0.5,
            color=YELLOW,
            fill_opacity=0.5
        )
        
        self.play(Create(axes), Create(curve))
        self.play(Create(rectangles))
        
        # Show convergence
        for dx in [0.2, 0.1, 0.05]:
            new_rects = axes.get_riemann_rectangles(
                curve, x_range=[0, 3], dx=dx,
                color=YELLOW, fill_opacity=0.5
            )
            self.play(Transform(rectangles, new_rects))

3.5: 3D Graphics & Transformations

Basic 3D Scene

class ThreeDDemo(ThreeDScene):
    def construct(self):
        # Set up 3D camera
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        
        # Create 3D objects
        axes = ThreeDAxes()
        sphere = Sphere(radius=1, color=BLUE)
        cube = Cube(side_length=2, color=RED)
        
        # Animate
        self.play(Create(axes))
        self.play(Create(sphere))
        self.wait(1)
        
        # Rotate camera
        self.begin_ambient_camera_rotation(rate=0.3)
        self.wait(3)
        self.stop_ambient_camera_rotation()
        
        # Transform
        self.play(Transform(sphere, cube))
        self.wait(1)

Parametric Surfaces

class ParametricSurfaceDemo(ThreeDScene):
    def construct(self):
        self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
        
        # Create parametric surface (torus)
        torus = Surface(
            lambda u, v: np.array([
                (2 + np.cos(v)) * np.cos(u),
                (2 + np.cos(v)) * np.sin(u),
                np.sin(v)
            ]),
            u_range=[0, TAU],
            v_range=[0, TAU],
            checkerboard_colors=[BLUE_D, BLUE_E]
        )
        
        self.play(Create(torus), run_time=3)
        self.begin_ambient_camera_rotation(rate=0.3)
        self.wait(5)

3.6: Final Project - Pythagorean Theorem

class PythagoreanTheorem(Scene):
    def construct(self):
        # Title
        title = Text("Pythagorean Theorem", font_size=48)
        title.to_edge(UP)
        self.play(Write(title))
        
        # Create right triangle
        triangle = Polygon(
            ORIGIN, RIGHT * 3, RIGHT * 3 + UP * 4,
            color=WHITE
        )
        triangle.shift(LEFT * 2 + DOWN * 1)
        
        self.play(Create(triangle))
        
        # Create squares on each side
        # Square on side a (height = 4)
        square_a = Square(side_length=4, color=BLUE, fill_opacity=0.5)
        square_a.next_to(triangle, LEFT, buff=0)
        square_a.align_to(triangle, DOWN)
        
        # Square on side b (base = 3)
        square_b = Square(side_length=3, color=GREEN, fill_opacity=0.5)
        square_b.next_to(triangle, DOWN, buff=0)
        square_b.align_to(triangle, LEFT)
        
        # Square on hypotenuse c (length = 5)
        square_c = Square(side_length=5, color=RED, fill_opacity=0.5)
        square_c.rotate(np.arctan(4/3))
        square_c.move_to(triangle.get_corner(UR) + UP * 2.5 + RIGHT * 2.5)
        
        self.play(FadeIn(square_a), FadeIn(square_b))
        self.wait(1)
        self.play(FadeIn(square_c))
        
        # Show equation
        equation = MathTex(r"a^2 + b^2 = c^2")
        equation.next_to(triangle, RIGHT, buff=1)
        
        values = MathTex(r"3^2 + 4^2 = 5^2")
        values.next_to(equation, DOWN)
        
        result = MathTex(r"9 + 16 = 25")
        result.next_to(values, DOWN)
        
        self.play(Write(equation))
        self.wait(1)
        self.play(Write(values))
        self.wait(1)
        self.play(Write(result))
        self.wait(2)

🏆 Advanced Project Ideas

Project 1: Fourier Series Visualize how sinusoids combine to approximate any periodic function

Project 2: Matrix Transformations Show how matrices rotate, scale, and shear vectors in 2D/3D

Project 3: Sorting Algorithms Animate bubble sort, merge sort, quick sort side by side

Project 4: Neural Network Visualize forward and backward propagation

Project 5: Mandelbrot Set Zoom into the famous fractal

📚 Resources & Next Steps

Learning More

Manim Community Docs: docs.manim.community
3Blue1Brown Channel: YouTube for inspiration
Theorem of Beethoven: Manim tutorials on YouTube

Where to Run Manim

Locally: Full control, best performance
Google Colab: Free, cloud-based
try.manim.community: Online editor

🎉 Congratulations!

You now know:

✅ Basic Manim setup and rendering
✅ Shapes, colors, and animations
✅ Mathematical functions and graphs
✅ LaTeX equations
✅ Calculus visualizations
✅ 3D graphics and transformations
✅ Complete project workflows

🚀 Your Journey Continues

You’ve completed all three chapters:

UV & Data Analysis - Professional Python workflows
Pygame - Game development
Manim - Mathematical animations

These skills open doors to:

🎓 Education technology
📊 Data visualization
🎮 Game development
🎨 Creative coding
🤖 Scientific computing

🌟 You’ve Leveled Up!

You’re no longer just learning programming—you’re creating experiences, teaching concepts, and building projects that inspire others.

The best way to solidify these skills: build something that excites YOU. Pick a project, start small, iterate, and share it with the world!

--- title: "Chapter 3.3-3.6: Manim Complete Guide" subtitle: "Math Functions, 3D Graphics, and Final Projects" format: live-html: code-tools: true execute: eval: false --- ::: {.quest-badge} 🎨 PROJECTS 3.3-3.6 | Difficulty: Intermediate-Advanced ::: ::: {.callout-note} Special Note: This project is designed for students who have completed the first chapter of CS Quests and are familiar with Python basics. If you're new to programming, consider starting with the earlier lessons before diving into this project. Another Special Note: This project requires a local Python environment for full functionality. While we provide examples and code snippets here, some features may not run directly in the browser. For the best experience, consider setting up the project on your own computer. ::: ## 3.3: Mathematical Functions & Graphs ### Plotting Functions ```python from manim import * class PlotFunction(Scene): def construct(self): # Create axes axes = Axes( x_range=[-5, 5, 1], y_range=[-3, 3, 1], axis_config={"color": BLUE} ) # Plot functions parabola = axes.plot(lambda x: x**2 / 4, color=RED) sine = axes.plot(lambda x: np.sin(x), color=GREEN) # Labels labels = axes.get_axis_labels(x_label="x", y_label="f(x)") # Animate self.play(Create(axes), Write(labels)) self.play(Create(parabola)) self.wait(1) self.play(Transform(parabola, sine)) self.wait(1) ``` ### LaTeX Equations ```python class LatexDemo(Scene): def construct(self): # Beautiful mathematical notation equation = MathTex(r"f(x) = \frac{1}{2}x^2 + 3x - 5") equation.scale(1.5) self.play(Write(equation)) self.wait(1) # Transform to derivative derivative = MathTex(r"f'(x) = x + 3") derivative.scale(1.5) self.play(TransformMatchingTex(equation, derivative)) self.wait(1) ``` ## 3.4: Calculus Visualizations ### Derivative Visualization ```python class DerivativeDemo(Scene): def construct(self): axes = Axes(x_range=[-3, 3], y_range=[-1, 9]) curve = axes.plot(lambda x: x**2, color=BLUE) # Moving tangent line def get_tangent_line(x): slope = 2 * x # derivative of x^2 point = axes.c2p(x, x**2) line = Line( point + LEFT * 1.5 + DOWN * slope * 1.5, point + RIGHT * 1.5 + UP * slope * 1.5, color=RED ) return line tangent = always_redraw(lambda: get_tangent_line(x_tracker.get_value())) x_tracker = ValueTracker(-2) self.add(axes, curve, tangent) self.play(x_tracker.animate.set_value(2), run_time=4) ``` ### Area Under Curve (Integration) ```python class IntegralDemo(Scene): def construct(self): axes = Axes(x_range=[0, 4], y_range=[0, 20]) curve = axes.plot(lambda x: x**2, color=BLUE) # Riemann rectangles rectangles = axes.get_riemann_rectangles( curve, x_range=[0, 3], dx=0.5, color=YELLOW, fill_opacity=0.5 ) self.play(Create(axes), Create(curve)) self.play(Create(rectangles)) # Show convergence for dx in [0.2, 0.1, 0.05]: new_rects = axes.get_riemann_rectangles( curve, x_range=[0, 3], dx=dx, color=YELLOW, fill_opacity=0.5 ) self.play(Transform(rectangles, new_rects)) ``` ## 3.5: 3D Graphics & Transformations ### Basic 3D Scene ```python class ThreeDDemo(ThreeDScene): def construct(self): # Set up 3D camera self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) # Create 3D objects axes = ThreeDAxes() sphere = Sphere(radius=1, color=BLUE) cube = Cube(side_length=2, color=RED) # Animate self.play(Create(axes)) self.play(Create(sphere)) self.wait(1) # Rotate camera self.begin_ambient_camera_rotation(rate=0.3) self.wait(3) self.stop_ambient_camera_rotation() # Transform self.play(Transform(sphere, cube)) self.wait(1) ``` ### Parametric Surfaces ```python class ParametricSurfaceDemo(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) # Create parametric surface (torus) torus = Surface( lambda u, v: np.array([ (2 + np.cos(v)) * np.cos(u), (2 + np.cos(v)) * np.sin(u), np.sin(v) ]), u_range=[0, TAU], v_range=[0, TAU], checkerboard_colors=[BLUE_D, BLUE_E] ) self.play(Create(torus), run_time=3) self.begin_ambient_camera_rotation(rate=0.3) self.wait(5) ``` ## 3.6: Final Project - Pythagorean Theorem ```python class PythagoreanTheorem(Scene): def construct(self): # Title title = Text("Pythagorean Theorem", font_size=48) title.to_edge(UP) self.play(Write(title)) # Create right triangle triangle = Polygon( ORIGIN, RIGHT * 3, RIGHT * 3 + UP * 4, color=WHITE ) triangle.shift(LEFT * 2 + DOWN * 1) self.play(Create(triangle)) # Create squares on each side # Square on side a (height = 4) square_a = Square(side_length=4, color=BLUE, fill_opacity=0.5) square_a.next_to(triangle, LEFT, buff=0) square_a.align_to(triangle, DOWN) # Square on side b (base = 3) square_b = Square(side_length=3, color=GREEN, fill_opacity=0.5) square_b.next_to(triangle, DOWN, buff=0) square_b.align_to(triangle, LEFT) # Square on hypotenuse c (length = 5) square_c = Square(side_length=5, color=RED, fill_opacity=0.5) square_c.rotate(np.arctan(4/3)) square_c.move_to(triangle.get_corner(UR) + UP * 2.5 + RIGHT * 2.5) self.play(FadeIn(square_a), FadeIn(square_b)) self.wait(1) self.play(FadeIn(square_c)) # Show equation equation = MathTex(r"a^2 + b^2 = c^2") equation.next_to(triangle, RIGHT, buff=1) values = MathTex(r"3^2 + 4^2 = 5^2") values.next_to(equation, DOWN) result = MathTex(r"9 + 16 = 25") result.next_to(values, DOWN) self.play(Write(equation)) self.wait(1) self.play(Write(values)) self.wait(1) self.play(Write(result)) self.wait(2) ``` ## 🏆 Advanced Project Ideas ::: {.challenge-box} **Project 1: Fourier Series** Visualize how sinusoids combine to approximate any periodic function **Project 2: Matrix Transformations** Show how matrices rotate, scale, and shear vectors in 2D/3D **Project 3: Sorting Algorithms** Animate bubble sort, merge sort, quick sort side by side **Project 4: Neural Network** Visualize forward and backward propagation **Project 5: Mandelbrot Set** Zoom into the famous fractal ::: ## 📚 Resources & Next Steps ### Learning More - **Manim Community Docs**: docs.manim.community - **3Blue1Brown Channel**: YouTube for inspiration - **Theorem of Beethoven**: Manim tutorials on YouTube ### Where to Run Manim - **Locally**: Full control, best performance - **Google Colab**: Free, cloud-based - **try.manim.community**: Online editor ### Share Your Work - **YouTube**: Create educational content - **Twitter/X**: Share short clips - **GitHub**: Open-source your animations ## 🎉 Congratulations! You now know: - ✅ Basic Manim setup and rendering - ✅ Shapes, colors, and animations - ✅ Mathematical functions and graphs - ✅ LaTeX equations - ✅ Calculus visualizations - ✅ 3D graphics and transformations - ✅ Complete project workflows ## 🚀 Your Journey Continues You've completed all three chapters: 1. **UV & Data Analysis** - Professional Python workflows 2. **Pygame** - Game development 3. **Manim** - Mathematical animations These skills open doors to: - 🎓 Education technology - 📊 Data visualization - 🎮 Game development - 🎨 Creative coding - 🤖 Scientific computing ::: {.success-box} **🌟 You've Leveled Up!** You're no longer just learning programming—you're creating experiences, teaching concepts, and building projects that inspire others. The best way to solidify these skills: **build something that excites YOU**. Pick a project, start small, iterate, and share it with the world! ::: --- ::: {.navigation-box} **Previous**: <a href="02-setup-manim.qmd" target="_blank">3.2 Setup Manim</a> | **Home**: <a href="../../all-quests.qmd" target="_blank">All Projects</a> :::