Manim Animation Examples & Ideas

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Trigonometry

Sine Wave Animation

Animate a sine wave showing the relationship between circular motion and wave patterns. Great for teaching periodic functions.

sine waveunit circleperiodic function

Cosine and Sine Relationship

Show how cosine and sine relate to each other as phase-shifted functions on a coordinate plane.

cosinephase shifttrigonometric functions

Geometry

Pythagorean Theorem Proof

Visual proof of the Pythagorean theorem using area rearrangement. One of the most elegant proofs in mathematics.

pythagorean theoremgeometric proofright triangle

Circle Area Derivation

Show how the area of a circle (πr²) can be derived by unwrapping it into triangles.

circle areapigeometry derivation

Calculus

Derivative as Tangent Slope

Visualize how the derivative represents the slope of the tangent line at any point on a curve.

derivativetangent lineslopecalculus

Riemann Sum Integration

Animate Riemann sums converging to the area under a curve as the number of rectangles increases.

integrationriemann sumarea under curve

Fundamental Theorem of Calculus

Show the connection between differentiation and integration visually.

fundamental theoremantiderivativecalculus connection

Linear Algebra

Matrix Transformation

Visualize how 2x2 matrices transform vectors and shapes in the plane.

matrix transformationlinear maprotation matrix

Eigenvectors Visualization

Show how eigenvectors remain on their span during a linear transformation.

eigenvectoreigenvaluelinear transformation

Dot Product Geometric Meaning

Illustrate the geometric interpretation of the dot product as projection.

dot productprojectionvector geometry

Advanced Topics

Fourier Series Visualization

Demonstrate how complex periodic waves can be built from simple sine waves.

fourier seriesharmonic analysiswave synthesis

Complex Number Multiplication

Show how multiplying complex numbers corresponds to rotation and scaling.

complex numberseuler formularotation

Taylor Series Approximation

Visualize how Taylor polynomials approximate functions near a point.

taylor seriespolynomial approximationconvergence

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