Visual Proof of the Pythagorean Theorem

Overview

A concise visual demonstration that the areas of the squares constructed on the legs of a right triangle combine to equal the area of the square on the hypotenuse, illustrating $a^{2}+b^{2}=c^{2}$.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3s	Fade‑in of a right triangle with legs labeled $a$ and $b$ and hypotenuse $c$. Simple highlight of the right angle.
2	Construct Squares	~6s	Squares are drawn outward on each side: a blue square on side $a$, a green square on side $b$, and a red square on side $c$. Each square’s side length matches its adjacent triangle side.
3	Area Highlight	~4s	The areas of the two smaller squares are shaded (e.g., semi‑transparent) and their combined area is shown as a numeric label $a^{2}+b^{2}$ (optional visual cue, not persistent text).
4	Rearrangement	~8s	The two smaller squares are cut into a few geometric pieces (standard dissection) and smoothly animated to re‑assemble inside the large square, perfectly filling it.
5	Reveal Equality	~3s	The assembled large square is highlighted, and the equation $a^{2}+b^{2}=c^{2}$ appears briefly in the caption area, then fades out as the scene ends.

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│              MAIN (primary visual)          │
│   – Triangle, squares, and moving pieces –   │
│                                             │
├─────────────────────────────────────────────┤
│  Caption (optional) – \\(a^{2}+b^{2}=c^{2}\\) – │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	Right triangle, three squares, dissection pieces, animated rearrangement	Central focus; occupies most of the frame
Caption	Equation $a^{2}+b^{2}=c^{2}$ shown only in final phase	Small footer; appears briefly

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Notes

• Assumed standard right‑triangle orientation (right angle at bottom‑left) for clarity.
• Used a classic 4‑piece dissection of the two smaller squares to fill the large square; other dissections are possible but this is the most common visual proof.
• No persistent on‑screen text except the final equation, adhering to the guideline to minimize text.
• Total animation time ~24 seconds, well within the 30‑second limit.
• Single Scene class will contain all phases sequentially.