Rohitg00 Manim Video Generator Math Visualizer

Math Visualizer Skill

The Math Visualizer brings mathematical concepts to life through precise, beautiful animations that reveal the structure and relationships within mathematics.

Mathematical Domains

Supported Areas

• Algebra: Equations, inequalities, polynomials
• Calculus: Derivatives, integrals, limits, series
• Geometry: Shapes, transformations, proofs
• Trigonometry: Functions, identities, unit circle
• Linear Algebra: Vectors, matrices, transformations
• Complex Analysis: Complex numbers, transformations
• Number Theory: Primes, sequences, patterns

Rules

rules/equation-presentation.md

How to present equations with proper pacing and emphasis.

rules/color-coding-math.md

Consistent color schemes for mathematical elements.

rules/graphing-best-practices.md

Creating clear, informative function graphs.

rules/proof-visualization.md

Step-by-step proof animations that build understanding.

Color Coding Standard

Templates

Equation Derivation

from manim import *

class EquationDerivation(Scene):
    def construct(self):
        # Initial equation
        eq1 = MathTex(r"x^2 + 2x + 1 = 0")
        self.play(Write(eq1))
        self.wait()

        # Transform step by step
        eq2 = MathTex(r"(x + 1)^2 = 0")
        eq3 = MathTex(r"x + 1 = 0")
        eq4 = MathTex(r"x = -1")

        # Show each transformation
        for new_eq in [eq2, eq3, eq4]:
            self.play(TransformMatchingTex(eq1, new_eq))
            self.wait()
            eq1 = new_eq

        # Highlight final answer
        box = SurroundingRectangle(eq4, color=GREEN, buff=0.2)
        self.play(Create(box))

Color-Coded Equation

from manim import *

class ColorCodedEquation(Scene):
    def construct(self):
        # Equation with color-coded parts
        equation = MathTex(
            r"f(", r"x", r") = ", r"a", r"x^2", r" + ", r"b", r"x", r" + ", r"c"
        )

        # Color code
        equation[1].set_color(BLUE)   # x
        equation[3].set_color(YELLOW) # a
        equation[4].set_color(BLUE)   # x^2
        equation[6].set_color(YELLOW) # b
        equation[7].set_color(BLUE)   # x
        equation[9].set_color(YELLOW) # c

        self.play(Write(equation))

        # Explain each part
        labels = [
            (equation[3], "coefficient"),
            (equation[1], "variable"),
            (equation[9], "constant")
        ]

        for part, label_text in labels:
            self.play(Indicate(part))
            label = Text(label_text, font_size=24).next_to(part, DOWN)
            self.play(Write(label))
            self.wait()
            self.play(FadeOut(label))

Function Graph with Animation

from manim import *

class FunctionGraph(Scene):
    def construct(self):
        # Create axes
        axes = Axes(
            x_range=[-4, 4, 1],
            y_range=[-2, 8, 1],
            x_length=8,
            y_length=5,
            axis_config={"include_tip": True}
        )
        labels = axes.get_axis_labels(x_label="x", y_label="y")

        self.play(Create(axes), Write(labels))

        # Function
        func = axes.plot(lambda x: x**2, color=BLUE)
        func_label = MathTex(r"f(x) = x^2", color=BLUE).to_corner(UR)

        self.play(Create(func), Write(func_label))

        # Show derivative
        deriv = axes.plot(lambda x: 2*x, color=GREEN)
        deriv_label = MathTex(r"f'(x) = 2x", color=GREEN).next_to(func_label, DOWN)

        self.play(Create(deriv), Write(deriv_label))

        # Tangent line demonstration
        x_tracker = ValueTracker(-2)

        tangent = always_redraw(lambda: axes.get_secant_slope_group(
            x=x_tracker.get_value(),
            graph=func,
            dx=0.01,
            secant_line_color=YELLOW,
            secant_line_length=4
        ))

        dot = always_redraw(lambda: Dot(
            axes.c2p(x_tracker.get_value(), x_tracker.get_value()**2),
            color=RED
        ))

        self.play(Create(tangent), Create(dot))
        self.play(x_tracker.animate.set_value(2), run_time=4)

3D Mathematical Surface

from manim import *

class Surface3D(ThreeDScene):
    def construct(self):
        # Set up camera
        self.set_camera_orientation(phi=75 * DEGREES, theta=-45 * DEGREES)

        # Create axes
        axes = ThreeDAxes(
            x_range=[-3, 3, 1],
            y_range=[-3, 3, 1],
            z_range=[-2, 2, 1]
        )

        # Create surface
        surface = Surface(
            lambda u, v: axes.c2p(u, v, np.sin(u) * np.cos(v)),
            u_range=[-PI, PI],
            v_range=[-PI, PI],
            resolution=(30, 30),
            fill_opacity=0.7
        )
        surface.set_fill_by_value(
            axes=axes,
            colorscale=[(RED, -1), (YELLOW, 0), (GREEN, 1)]
        )

        # Animate
        self.play(Create(axes))
        self.play(Create(surface), run_time=3)
        self.begin_ambient_camera_rotation(rate=0.2)
        self.wait(5)

Geometric Proof

from manim import *

class PythagoreanProof(Scene):
    def construct(self):
        # Create right triangle
        triangle = Polygon(
            ORIGIN, RIGHT * 3, RIGHT * 3 + UP * 4,
            color=WHITE, fill_opacity=0.3
        )

        # Labels
        a_label = MathTex("a").next_to(triangle, DOWN)
        b_label = MathTex("b").next_to(triangle, RIGHT)
        c_label = MathTex("c").move_to(
            (ORIGIN + RIGHT * 3 + UP * 4) / 2 + LEFT * 0.5 + UP * 0.3
        )

        self.play(Create(triangle))
        self.play(Write(a_label), Write(b_label), Write(c_label))

        # Show squares on each side
        sq_a = Square(side_length=3, color=BLUE, fill_opacity=0.5)
        sq_a.next_to(triangle, DOWN, buff=0)

        sq_b = Square(side_length=4, color=GREEN, fill_opacity=0.5)
        sq_b.next_to(triangle, RIGHT, buff=0)

        self.play(Create(sq_a), Create(sq_b))

        # Area labels
        area_a = MathTex(r"a^2", color=BLUE).move_to(sq_a)
        area_b = MathTex(r"b^2", color=GREEN).move_to(sq_b)

        self.play(Write(area_a), Write(area_b))

        # Conclusion
        theorem = MathTex(r"a^2 + b^2 = c^2").to_edge(UP)
        box = SurroundingRectangle(theorem, color=GOLD)

        self.play(Write(theorem), Create(box))

LaTeX Quick Reference

Common Expressions

% Fractions
\frac{a}{b}

% Square root
\sqrt{x}  \sqrt[n]{x}

% Summation
\sum_{i=1}^{n} x_i

% Integral
\int_{a}^{b} f(x) \, dx

% Limit
\lim_{x \to \infty} f(x)

% Matrix
\begin{pmatrix} a & b \\ c & d \end{pmatrix}

% Partial derivative
\frac{\partial f}{\partial x}

Greek Letters

\alpha \beta \gamma \delta \epsilon
\theta \lambda \mu \pi \sigma \omega
\Gamma \Delta \Theta \Lambda \Sigma \Omega

Best Practices

1. Reveal equations gradually - Build up complex equations piece by piece
2. Use consistent notation - Same symbol = same meaning throughout
3. Annotate meaningfully - Labels should clarify, not clutter
4. Show, don't just state - Animate the mathematical relationships
5. Connect to intuition - Bridge abstract math to visual understanding

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