/manim-composer

Narrative Patterns for Math Explainers

Common structures used in effective 3Blue1Brown-style videos.

Pattern 1: Mystery → Investigation → Resolution

Structure:

1. Present a puzzling result or paradox
2. Investigate why it's true through visual exploration
3. Reveal the underlying principle
4. Show how the principle generalizes

Example topics: Euler's identity, Bayes theorem, infinite series paradoxes

Opening hooks:

• "What does it even mean to raise a number to an imaginary power?"
• "This equation looks wrong, but it's actually true..."
• "Most people get this probability question wrong..."

Pattern 2: Build Up → Payoff

Structure:

1. Introduce simple building blocks
2. Combine them to create something complex
3. Show the beautiful/surprising result
4. Reflect on why it works

Example topics: Fourier series, neural networks, linear algebra

Opening hooks:

• "Let's start with something simple..."
• "Each piece here is easy, but together they do something remarkable..."

Pattern 3: Two Perspectives → Unity

Structure:

1. Show concept from perspective A (e.g., algebraic)
2. Show same concept from perspective B (e.g., geometric)
3. Reveal they're the same thing
4. Explore implications of this connection

Example topics: Dot product, determinants, complex multiplication

Opening hooks:

• "There are two ways to think about this..."
• "These seem like completely different ideas, but..."

Pattern 4: Wrong → Less Wrong → Right

Structure:

1. Present common misconception or naive approach
2. Show why it fails
3. Refine the approach
4. Arrive at correct understanding

Example topics: Limits, probability distributions, definitions

Opening hooks:

• "Your first instinct here is probably wrong..."
• "The obvious approach doesn't quite work..."

Pattern 5: Specific → General

Structure:

1. Solve a specific concrete example
2. Notice patterns in the solution
3. Abstract to general principle
4. Apply to new situations

Example topics: Derivatives, group theory, algorithm analysis

Opening hooks:

• "Let's work through a specific example..."
• "Once you see the pattern here, it shows up everywhere..."

Pattern 6: History as Narrative

Structure:

1. Present the problem as historically encountered
2. Follow the journey of discovery
3. Show key insights that led to breakthroughs
4. Connect to modern understanding

Example topics: Calculus, cryptography, quantum mechanics

Opening hooks:

• "Imagine you're a mathematician in the 1600s..."
• "This problem stumped the greatest minds for centuries..."

Combining Patterns

Most effective videos combine multiple patterns:

• Mystery hook + Build Up explanation
• Two Perspectives + Specific → General examples
• Wrong → Right + History narrative

Pacing Guidelines

Emotional Arc

Every video should have emotional beats:

1. Curiosity (opening) - Why should I care?
2. Confusion (early) - This is harder than it looks
3. Partial clarity (middle) - I'm starting to see...
4. Aha moment (climax) - Oh! That's beautiful!
5. Satisfaction (end) - Now I truly understand