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
How to present equations with proper pacing and emphasis.
Consistent color schemes for mathematical elements.
Creating clear, informative function graphs.
Step-by-step proof animations that build understanding.
Color Coding Standard
| Element | Color | Hex |
|---|
| Variables (x, y) | BLUE | #58C4DD |
| Constants | YELLOW | #FFFF00 |
| Operators | WHITE | #FFFFFF |
| Key Terms | GREEN | #83C167 |
| Equals/Results | GOLD | #FFD700 |
| Negative/Subtract | RED | #FC6255 |
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
- Reveal equations gradually - Build up complex equations piece by piece
- Use consistent notation - Same symbol = same meaning throughout
- Annotate meaningfully - Labels should clarify, not clutter
- Show, don't just state - Animate the mathematical relationships
- Connect to intuition - Bridge abstract math to visual understanding