3Blue1Brown Style Mathematical Animations

Use this skill when creating mathematical animations, visualizations, or educational videos about math, algorithms, or deep learning.

Core Philosophy

“The goal is not to animate math, but to build understanding.”

1. Intuition Before Formalism — Build visual understanding before showing formulas
2. Why Before What — Motivate concepts before defining them
3. Concrete Before Abstract — Start with specific examples, then generalize
4. Show, Don’t Tell — Let the visual do the explaining

When to Use

• Creating mathematical animations with Manim
• Explaining algorithms visually
• Building deep learning visualizations
• Producing educational video content

AI-Guided Planning (REQUIRED)

Before starting any video, follow this workflow:

Step 1: Draft Plan Internally

When user requests an animation:

• Understand the topic
• Draft content structure
• Identify visual elements needed

Step 2: Ask User Preferences

Use AskUserQuestion tool to gather preferences:

questions = [
    {
        "question": "Do you want narration audio in this video?",
        "header": "Audio",
        "options": [
            {"label": "With Audio (Recommended)", "description": "TTS narration synced to animation"},
            {"label": "Without Audio", "description": "Animation only, add your own audio later"}
        ],
        "multiSelect": False
    },
    {
        "question": "How long should the video be?",
        "header": "Duration",
        "options": [
            {"label": "Short (30-60s)", "description": "Quick concept overview"},
            {"label": "Medium (1-2 min)", "description": "Standard explanation"},
            {"label": "Long (3+ min)", "description": "Deep dive with examples"},
            {"label": "Auto (Recommended)", "description": "Let content determine length"}
        ],
        "multiSelect": False
    }
]

Step 3: Present Plan for Approval

Show the content plan before coding:

📋 Animation Plan: [Topic]

1. Hook: [Opening question]
2. Setup: [Context]
3. Core: [Main explanation]
4. Example: [Demonstration]
5. Takeaway: [Conclusion]

Settings: Audio=Yes, Duration=Auto (~70s)

Shall I proceed?

Step 4: Execute Based on Choices

Key Principles

Duration is NOT Fixed

# ❌ WRONG: Force fixed duration
duration = 60  # arbitrary

# ✅ RIGHT: Content determines duration
script = write_explanation(topic)
duration = measure(script)  # natural length

Always Ask, Never Assume

• Audio preference
• Duration preference
• Detail level (if relevant)

Rules Index

Highest Priority: Quality & Planning

High Priority: Pedagogy & Content

Visual Design

Domain: Linear Algebra

Domain: Statistics & Probability

Domain: Deep Learning

Domain: CNN

Technical

Example Interaction

User: "quick sort 애니메이션 만들어줘"

AI: [Internal: Draft plan for QuickSort]

AI: [AskUserQuestion]
    "I'll create a QuickSort animation. Quick questions:

    1. Audio: With narration / Without
    2. Duration: Short / Medium / Auto"

User: "audio 있고, auto로"

AI: "Here's my plan:

    📋 QuickSort Animation

    1. Hook: How do we sort efficiently?
    2. Setup: Unsorted array
    3. Core: Pivot selection, partitioning
    4. Example: Sort [8,3,7,1,5,2]
    5. Takeaway: O(n log n) average

    Duration: ~90s (based on narration)

    Proceed?"

User: "네"

AI: [Executes workflow]
    → Generates TTS
    → Measures timing
    → Creates animation
    → Renders & combines
    → Shows result

Quick Start Code

from manim import *

class ExplanationScene(Scene):
    def construct(self):
        self.camera.background_color = "#1c1c1c"

        # Sync to audio timing (if audio enabled)
        # TIMING = {...}  # from TTS generation

        # 1. Hook: Pose the question
        # 2. Intuition: Build visual understanding
        # 3. Formalize: Show the math
        # 4. Verify: Demonstrate with example