The Pythagorean Theorem
Audience: Middle SchoolCategory: Math
Description
Presents the visual square-area proof of the Pythagorean Theorem using a 3-4-5 right triangle. Students see squares growing on each side and observe that the two smaller areas add up to the largest area, giving intuition for aΒ² + bΒ² = cΒ².
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The Pythagorean Theorem
Description
Presents the visual square-area proof of the Pythagorean Theorem using a 3-4-5 right triangle. Students see squares growing on each side and observe that the two smaller areas add up to the largest area, giving intuition for aΒ² + bΒ² = cΒ².
Phases
| # | Phase Name | Duration | Description |
|---|---|---|---|
| 1 | Draw the Triangle | 7s | Animate a right triangle with legs a=3 (vertical), b=4 (horizontal), hypotenuse c=5. Label each side. |
| 2 | Grow Squares | 12s | Animate a square growing on each side in sequence: blue on a, orange on b, green on c. |
| 3 | Show Areas | 8s | Label each square with its area (9, 16, 25). Animate 9 + 16 box highlighting = 25. |
| 4 | Formula | 6s | Display MathTex aΒ² + bΒ² = cΒ² with values substituted (9 + 16 = 25). |
| 5 | Summary | 5s | Recap the theorem in words and formula. |
Layout
+------------------------------------------------------+
| [Title: The Pythagorean Theorem] |
| |
| [Square on c] |
| |
| [Sq ] /| |
| [ on ] / | |
| [ a ] / | a=3 |
| / | |
| +----+ |
| b=4 |
| [Square on b] |
| |
| [Formula display] |
+------------------------------------------------------+
Area Descriptions
| Area | Content | Notes |
|---|---|---|
| Center | Right triangle | 3-4-5, right angle at bottom-right |
| Left of triangle | Square on side a | Blue fill |
| Below triangle | Square on side b | Orange fill |
| Upper-right | Square on hypotenuse c | Green fill |
| Bottom | Area equations and formula | Updates per phase |
Assets & Dependencies
- Fonts: LaTeX / sans-serif
- Colors:
- Side a: BLUE
- Side b: ORANGE
- Hypotenuse c: GREEN
- Right angle marker: WHITE
- Background: #1a1a2e
- Manim version: ManimCE 0.19.1
Notes
- Scale the triangle so it fits well. One unit β 0.5 scene units.
- Squares are Polygon objects or Square objects rotated to align with each side.
- The visual proof is the main feature; the formula reinforces it.