Chapter 3.3-3.6: Manim Complete Guide

Math Functions, 3D Graphics, and Final Projects

🎨 PROJECTS 3.3-3.6 | Difficulty: Intermediate-Advanced

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 ::: ## 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**: [3.2 Setup Manim](02-setup-manim.qmd) | **Home**: [All Projects](../../all-quests.qmd) :::