# Pythagorean Theorem Animation — Plan

## Overview
- **Topic**: a² + b² = c²
- **Hook**: Why does the longest side squared equal the sum of the other two sides squared?
- **Aha moment**: When the three squares tile perfectly and two smaller ones fill the large one exactly
- **Target audience**: Students learning geometry, anyone who's memorized but never *seen* why
- **Length**: ~90 seconds
- **Resolution**: 480p (draft)

## Color Palette — Classic 3B1B
- Background: `#1C1C1C`
- PRIMARY: `#58C4DD` (BLUE) — a-side, a² square
- SECONDARY: `#83C167` (GREEN) — b-side, b² square
- ACCENT: `#FFFF00` (YELLOW) — c-side, c² square, highlights
- WHITE: — labels, axes
- RED: `#FF6B6B` — equation text accent

## Arc: Discovery

---

## Scene 1: Title (~6s)
**Purpose**: Hook — pose the question

### Visual elements
- Title: "The Pythagorean Theorem"
- Subtitle equation: a² + b² = c²

### Animation
1. Title fades in
2. Equation appears below

### Subtitle
"Proved not by numbers — but by area."

---

## Scene 2: The Triangle (~15s)
**Purpose**: Introduce the right triangle with labeled sides

### Visual elements
- Right triangle, vertices at (0,0), (4,0), (0,3)
- Side a = 3 (vertical, left)
- Side b = 4 (horizontal, bottom)
- Side c = 5 (hypotenuse, diagonal)
- Right angle marker at (0,0)

### Animation
1. Triangle outline appears (Create)
2. Label "a" appears on vertical side with brace
3. Label "b" appears on horizontal side with brace
4. Label "c" appears on hypotenuse
5. "a = 3, b = 4, c = 5" appears at bottom

### Subtitle
"A right triangle with sides 3, 4, and 5."

---

## Scene 3: Three Squares (~20s)
**Purpose**: Show the three squares built on each side

### Visual elements
- Square on a (blue), area = 9
- Square on b (green), area = 16
- Square on c (yellow), area = 25
- Each square labeled with its area

### Animation
1. Square on a slides/fades in next to triangle
2. "a² = 9" label appears
3. Square on b slides/fades in
4. "b² = 16" label appears
5. Square on c slides/fades in
6. "c² = 25" label appears

### Subtitle
"Each side builds its own square. The areas are no coincidence."

---

## Scene 4: The Proof — Tilin (~25s)
**Purpose**: The geometric proof — two small squares perfectly fill the large one

### Visual elements
- Large yellow square (c²) shown as a container
- Blue square (a²) and green square (b²) tiled inside it
- Pieces labeled "a²" and "b²"
- Perfect tile fit demonstrated

### Animation
1. Large yellow square shown as outline
2. Blue square (a²) pieces slide in from left
3. Green square (b²) pieces slide in from bottom
4. Both fit perfectly — no gaps, no overlap
5. Labels "a² + b² = c²" appear

### Subtitle
"No gaps. No overlap. Two hundred proof squares filling one."

---

## Scene 5: The Equation (~15s)
**Purpose**: The algebraic statement of what we just saw

### Visual elements
- a² + b² = c² centered
- Substitution: 9 + 16 = 25
- Final result

### Animation
1. a² + b² = c² fades in
2. Below: 3² + 4² = 5²
3. Below: 9 + 16 = 25
4. All three highlighted in sequence

### Subtitle
"3 squared plus 4 squared equals 5 squared."

---

## Scene 6: The Silence (~10s)
**Purpose**: Let the beauty sink in

### Visual elements
- Triangle + equation
- Blank space

### Animation
1. Clean fade in of the theorem statement
2. Pause

### Subtitle
"Proved 2500 years ago. Still perfect."