# 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..."

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## 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..."

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## 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..."

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## 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

| Video Length | Intro Hook | Main Content | Recap/Implications |
|--------------|------------|--------------|-------------------|
| 5-10 min     | 30-60s     | 4-8 min      | 30-60s            |
| 15-20 min    | 1-2 min    | 12-16 min    | 1-2 min           |
| 30+ min      | 2-3 min    | 24-26 min    | 2-4 min           |

## 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
