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The Pythagorean Theorem

受眾: Middle School類別: Math

簡介

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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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.

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.

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 ≈ 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.