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 a² + b² = c².

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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 a² + b² = c² with values substituted (9 + 16 = 25).
5	Summary	5s	Recap the theorem in words and formula.

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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

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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

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Notes

• Scale the triangle so it fits well. One unit ≈ 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.